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br-j19
Experiments are often composed of several identical trials , and sometimes experiments themselves are repeated .
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br-j19
In the marksmanship example , a trial consists of `` one round shot at a target '' with outcome either one bull's-eye (success) or none (failure).
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br-j19
Further , an experiment might consist of five rounds , and several sets of five rounds might be regarded as a super experiment composed of several repetitions of the five round experiment .
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br-j19
If three dice are tossed , a trial is one toss of one die and the experiment is composed of three trials .
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br-j19
Or , what amounts to the same thing , if one die is tossed three times , each toss is a trial , and the three tosses form the experiment .
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br-j19
Mathematically , we shall not distinguish the experiment of three dice tossed once from that of one die tossed three times .
<NONE>
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br-j19
These examples are illustrative of the use of the words `` trial '' and `` experiment '' as they are used in this chapter , but they are quite flexible words and it is well not to restrict them too narrowly .
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br-j19
Ten students act as managers for a high-school football team , and of these managers a proportion p are licensed drivers .
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br-j19
Each Friday one manager is chosen by lot to stay late and load the equipment on a truck .
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br-j19
On three Fridays the coach has needed a driver .
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br-j19
Considering only these Fridays , what is the probability that the coach had drivers all 3 times ?
<NONE>
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br-j19
Exactly 2 times ?
<NONE>
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[ "0", "1", "2", "3" ]
[ "0.344", "0.301", "0.360", "0.458" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
1 time ?
<NONE>
<NONE>
[ "1", "fois", "?" ]
[ "<NONE>", "time%1:11:00::", "<NONE>" ]
[ "<NONE>", "time%1:11:00", "<NONE>" ]
[ "<NONE>", "1", "2" ]
[ "<NONE>", "0.401", "0.523" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
br-j19
0 time ?
<NONE>
<NONE>
[ "0", "temps", "?" ]
[ "<NONE>", "time%1:11:00::", "<NONE>" ]
[ "<NONE>", "time%1:11:00", "<NONE>" ]
[ "<NONE>", "1", "2" ]
[ "<NONE>", "0.438", "0.408" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Note that there are 3 trials of interest .
<NONE>
<NONE>
[ "Notez", "qu&apos;", "il", "y", "a", "3", "essais", "d&apos;", "intérêt", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:04::", "3%3:00:00:cardinal:00", "trial%1:04:00::", "<NONE>", "interest%1:09:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:04", "3%3:00:00:cardinal:00", "trial%1:04:00", "<NONE>", "interest%1:09:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "2", "3", "4", "5", "<NONE>", "7", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "0.222", "0.216", "0.272", "0.394", "<NONE>", "0.333", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Each trial consists of choosing a student manager at random .
<NONE>
<NONE>
[ "Chaque", "essai", "consiste", "à", "choisir", "un", "directeur", "étudiant", "au", "hasard", "." ]
[ "<NONE>", "trial%1:04:00::", "<NONE>", "<NONE>", "choose%2:31:00::", "<NONE>", "<NONE>", "student%1:18:00::", "<NONE>", "at_random%4:02:00::", "<NONE>" ]
[ "<NONE>", "trial%1:04:00", "<NONE>", "<NONE>", "choose%2:31:00", "<NONE>", "<NONE>", "student%1:18:00", "<NONE>", "at_random%4:02:00", "<NONE>" ]
[ "<NONE>", "1", "2", "<NONE>", "4", "<NONE>", "<NONE>", "6", "<NONE>", "9", "10" ]
[ "<NONE>", "0.404", "0.294", "<NONE>", "0.314", "<NONE>", "<NONE>", "0.433", "<NONE>", "0.466", "0.432" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The 2 possible outcomes on each trial are `` driver '' or `` nondriver '' .
<NONE>
<NONE>
[ "Les", "deux", "résultats", "possibles", "de", "chaque", "essai", "sont", "le", "rôle", "moteur", "et", "le", "rôle", "." ]
[ "be%2:42:06::", "2%3:00:00:cardinal:00", "<NONE>", "possible%3:00:04::", "<NONE>", "each%3:00:00:all:00", "trial%1:04:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "be%2:42:06", "2%3:00:00:cardinal:00", "<NONE>", "possible%3:00:04", "<NONE>", "each%3:00:00:all:00", "trial%1:04:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "7", "1", "<NONE>", "2", "4", "5", "6", "<NONE>", "<NONE>", "8", "<NONE>", "10", "<NONE>", "12", "14" ]
[ "0.201", "0.337", "<NONE>", "0.326", "0.209", "0.208", "0.333", "<NONE>", "<NONE>", "0.449", "<NONE>", "0.494", "<NONE>", "0.359", "0.278" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Since the choice is by lot each week , the outcomes of different trials are independent .
<NONE>
<NONE>
[ "Étant", "donné", "que", "le", "choix", "se", "fait", "par", "tirage", "au", "sort", "chaque", "semaine", ",", "les", "résultats", "des", "différents", "essais", "sont", "indépendants", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "choice%1:04:00::", "<NONE>", "be%2:42:04::", "<NONE>", "<NONE>", "lot%1:06:00::", "<NONE>", "<NONE>", "each_week%4:02:00::", "<NONE>", "<NONE>", "outcome%1:11:00::", "<NONE>", "different%3:00:00:other:00", "trial%1:04:00::", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "choice%1:04:00", "<NONE>", "be%2:42:04", "<NONE>", "<NONE>", "lot%1:06:00", "<NONE>", "<NONE>", "each_week%4:02:00", "<NONE>", "<NONE>", "outcome%1:11:00", "<NONE>", "different%3:00:00:other:00", "trial%1:04:00", "<NONE>", "independent...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "2", "<NONE>", "3", "<NONE>", "<NONE>", "5", "<NONE>", "<NONE>", "7", "<NONE>", "<NONE>", "10", "<NONE>", "12", "13", "<NONE>", "15", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.340", "<NONE>", "0.277", "<NONE>", "<NONE>", "0.509", "<NONE>", "<NONE>", "0.428", "<NONE>", "<NONE>", "0.324", "<NONE>", "0.311", "0.340", "<NONE>", "0.388", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The managers stay the same , so that * * f is the same for all weeks .
<NONE>
<NONE>
[ "Les", "gestionnaires", "restent", "les", "mêmes", ",", "de", "sorte", "que", "*", "*", "f", "est", "le", "même", "pour", "toutes", "les", "semaines", "." ]
[ "<NONE>", "manager%1:18:01::", "stay%2:30:00::", "<NONE>", "same%3:00:00:unchanged:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "same%3:00:00:unchanged:00", "<NONE>", "<NONE>", "<NONE>", "week%1:28:00::", "<NONE>" ]
[ "<NONE>", "manager%1:18:01", "stay%2:30:00", "<NONE>", "same%3:00:00:unchanged:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "same%3:00:00:unchanged:00", "<NONE>", "<NONE>", "<NONE>", "week%1:28:00", "<NONE>" ]
[ "<NONE>", "1", "2", "3", "4", "<NONE>", "6", "<NONE>", "7", "8", "9", "10", "<NONE>", "<NONE>", "13", "14", "15", "<NONE>", "16", "<NONE>" ]
[ "<NONE>", "0.351", "0.292", "0.243", "0.289", "<NONE>", "0.296", "<NONE>", "0.201", "0.285", "0.284", "0.335", "<NONE>", "<NONE>", "0.253", "0.181", "0.267", "<NONE>", "0.402", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
We now generalize these ideas for general binomial experiments .
<NONE>
<NONE>
[ "Nous", "généralisons", "maintenant", "ces", "idées", "pour", "des", "expériences", "binomiales", "générales", "." ]
[ "<NONE>", "generalize%2:32:01::", "<NONE>", "<NONE>", "idea%1:09:00::", "<NONE>", "<NONE>", "experiment%1:04:00::", "binomial%3:01:00::", "general%3:00:00::", "<NONE>" ]
[ "<NONE>", "generalize%2:32:01", "<NONE>", "<NONE>", "idea%1:09:00", "<NONE>", "<NONE>", "experiment%1:04:00", "binomial%3:01:00", "general%3:00:00", "<NONE>" ]
[ "<NONE>", "2", "<NONE>", "3", "4", "<NONE>", "5", "8", "7", "6", "<NONE>" ]
[ "<NONE>", "0.308", "<NONE>", "0.222", "0.361", "<NONE>", "0.260", "0.344", "0.386", "0.394", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
For an experiment to qualify as a binomial experiment , it must have four properties: (1) there must be a fixed number of trials , (2) each trial must result in a `` success '' or a `` failure '' (a binomial trial), (3) all trials must have identical probabilities of success , (4) the trials must be independent of each other .
<NONE>
<NONE>
[ "Pour", "qu&apos;", "une", "expérience", "puisse", "être", "considérée", "comme", "une", "expérience", "binomiale", ",", "elle", "doit", "avoir", "quatre", "propriétés", ":", "le", "domaine", "1", ")", ",", "il", "doit", "y", "avoir", "un", "nombre", "fixe",...
[ "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "<NONE>", "qualify%2:42:00::", "<NONE>", "<NONE>", "<NONE>", "binomial%3:01:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "four%3:00:00:cardinal:00", "property%1:07:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>",...
[ "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00", "<NONE>", "<NONE>", "qualify%2:42:00", "<NONE>", "<NONE>", "<NONE>", "binomial%3:01:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "four%3:00:00:cardinal:00", "property%1:07:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NON...
[ "<NONE>", "1", "3", "2", "<NONE>", "<NONE>", "4", "<NONE>", "<NONE>", "6", "7", "9", "10", "11", "<NONE>", "13", "14", "<NONE>", "15", "<NONE>", "<NONE>", "15", "15", "16", "17", "<NONE>", "18", "<NONE>", "21", "20", "<NONE>", "23", "<NONE>", "25", ...
[ "<NONE>", "0.133", "0.158", "0.180", "<NONE>", "<NONE>", "0.176", "<NONE>", "<NONE>", "0.116", "0.186", "0.130", "0.092", "0.154", "<NONE>", "0.178", "0.257", "<NONE>", "0.381", "<NONE>", "<NONE>", "0.138", "0.140", "0.100", "0.140", "<NONE>", "0.136", "<NONE>",...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Below we use our earlier examples to describe and illustrate these four properties .
<NONE>
<NONE>
[ "Nous", "utilisons", "ci", "@-@", "dessous", "nos", "exemples", "antérieurs", "pour", "décrire", "et", "illustrer", "ces", "quatre", "propriétés", "." ]
[ "<NONE>", "<NONE>", "use%2:34:01::", "<NONE>", "<NONE>", "<NONE>", "example%1:09:00::", "earlier%3:00:00:early:00", "<NONE>", "describe%2:32:00::", "<NONE>", "illustrate%2:32:00::", "<NONE>", "four%3:00:00:cardinal:00", "property%1:07:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "use%2:34:01", "<NONE>", "<NONE>", "<NONE>", "example%1:09:00", "earlier%3:00:00:early:00", "<NONE>", "describe%2:32:00", "<NONE>", "illustrate%2:32:00", "<NONE>", "four%3:00:00:cardinal:00", "property%1:07:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "2", "<NONE>", "<NONE>", "<NONE>", "5", "4", "6", "7", "8", "9", "<NONE>", "11", "12", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.231", "<NONE>", "<NONE>", "<NONE>", "0.238", "0.266", "0.155", "0.286", "0.260", "0.323", "<NONE>", "0.324", "0.370", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
We also give , for each property , an example where the property is absent .
<NONE>
<NONE>
[ "Nous", "donnons", "aussi", ",", "pour", "chaque", "bien", ",", "un", "exemple", "où", "le", "bien", "est", "absent", "." ]
[ "<NONE>", "give%2:40:07::", "<NONE>", "also%4:02:00::", "<NONE>", "each%3:00:00:all:00", "property%1:07:00::", "<NONE>", "<NONE>", "example%1:09:00::", "<NONE>", "<NONE>", "property%1:07:00::", "<NONE>", "absent%3:00:00::", "<NONE>" ]
[ "<NONE>", "give%2:40:07", "<NONE>", "also%4:02:00", "<NONE>", "each%3:00:00:all:00", "property%1:07:00", "<NONE>", "<NONE>", "example%1:09:00", "<NONE>", "<NONE>", "property%1:07:00", "<NONE>", "absent%3:00:00", "<NONE>" ]
[ "<NONE>", "2", "<NONE>", "1", "4", "5", "6", "<NONE>", "<NONE>", "9", "10", "<NONE>", "12", "<NONE>", "14", "<NONE>" ]
[ "<NONE>", "0.275", "<NONE>", "0.181", "0.231", "0.313", "0.357", "<NONE>", "<NONE>", "0.349", "0.224", "<NONE>", "0.319", "<NONE>", "0.376", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The language and notation introduced are standard throughout the chapter .
<NONE>
<NONE>
[ "Le", "langage", "et", "la", "notation", "introduits", "sont", "uniformes", "dans", "tout", "le", "chapitre", "." ]
[ "<NONE>", "language%1:10:00::", "<NONE>", "<NONE>", "notation%1:10:00::", "introduce%2:32:00::", "<NONE>", "standard%3:00:02::", "<NONE>", "<NONE>", "<NONE>", "chapter%1:10:00::", "<NONE>" ]
[ "<NONE>", "language%1:10:00", "<NONE>", "<NONE>", "notation%1:10:00", "introduce%2:32:00", "<NONE>", "standard%3:00:02", "<NONE>", "<NONE>", "<NONE>", "chapter%1:10:00", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "<NONE>", "3", "4", "<NONE>", "6", "<NONE>", "7", "<NONE>", "9", "<NONE>" ]
[ "<NONE>", "0.333", "<NONE>", "<NONE>", "0.476", "0.315", "<NONE>", "0.330", "<NONE>", "0.440", "<NONE>", "0.360", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
For the marksman , we study sets of five shots (* * f); for the mice , we restrict attention to litters of eight (* * f); and for the aces , we toss three dice (* * f).
<NONE>
<NONE>
[ "Pour", "le", "tireur", ",", "nous", "étudions", "des", "séries", "de", "cinq", "clichés", ".", "Pour", "les", "souris", ",", "nous", "limitons", "l&apos;", "attention", "à", "des", "portées", "de", "huit", "heures", "*", "*", "f", ",", "et", "pour", "...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Toss a die until an ace appears .
<NONE>
<NONE>
[ "Cessez", "de", "mourir", "jusqu", "&quot;", "à", "ce", "qu&apos;", "un", "as", "apparaisse", "." ]
[ "<NONE>", "<NONE>", "die%1:06:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "ace%1:23:00::", "appear%2:30:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "die%1:06:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "ace%1:23:00", "appear%2:30:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "2", "<NONE>", "3", "<NONE>", "<NONE>", "4", "<NONE>", "5", "6", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.542", "<NONE>", "0.465", "<NONE>", "<NONE>", "0.206", "<NONE>", "0.529", "0.419", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Here the number of trials is a random variable , not a fixed number .
<NONE>
<NONE>
[ "Dans", "ce", "cas", ",", "le", "nombre", "d&apos;", "essais", "est", "une", "variable", "aléatoire", "et", "non", "un", "nombre", "fixe", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "number%1:07:00::", "<NONE>", "trial%1:04:00::", "<NONE>", "be%2:42:03::", "random_variable%1:09:00::", "random_variable%1:09:00::", "<NONE>", "not%4:02:00::", "<NONE>", "number%1:07:00::", "fixed%3:00:00:determinate:01", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "number%1:07:00", "<NONE>", "trial%1:04:00", "<NONE>", "be%2:42:03", "random_variable%1:09:00", "random_variable%1:09:00", "<NONE>", "not%4:02:00", "<NONE>", "number%1:07:00", "fixed%3:00:00:determinate:01", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "2", "<NONE>", "4", "<NONE>", "5", "8", "7", "<NONE>", "10", "<NONE>", "13", "12", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.349", "<NONE>", "0.349", "<NONE>", "0.179", "0.231", "0.364", "<NONE>", "0.319", "<NONE>", "0.229", "0.344", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Each of the n trials is either a success or a failure .
<NONE>
<NONE>
[ "Chacun", "des", "n", "essais", "est", "soit", "un", "succès", ",", "soit", "un", "échec", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "trial%1:04:00::", "<NONE>", "<NONE>", "<NONE>", "success%1:11:00::", "<NONE>", "<NONE>", "<NONE>", "failure%1:11:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "trial%1:04:00", "<NONE>", "<NONE>", "<NONE>", "success%1:11:00", "<NONE>", "<NONE>", "<NONE>", "failure%1:11:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "3", "4", "<NONE>", "6", "<NONE>", "8", "<NONE>", "9", "<NONE>", "11", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.394", "0.377", "<NONE>", "0.231", "<NONE>", "0.316", "<NONE>", "0.299", "<NONE>", "0.358", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
`` Success '' and `` failure '' are just convenient labels for the two categories of outcomes when we talk about binomial trials in general .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
These words are more expressive than labels like `` A '' and `` not - A '' .
<NONE>
<NONE>
[ "Ces", "mots", "sont", "plus", "éloquents", "que", "des", "étiquettes", "comme", "&quot;", "À", "&quot;", "et", "&quot;", "Non", "-", "A", "&quot;", "." ]
[ "<NONE>", "word%1:10:00::", "<NONE>", "more%3:00:01::", "expressive%3:00:00:communicative:00", "<NONE>", "<NONE>", "label%1:10:01::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "word%1:10:00", "<NONE>", "more%3:00:01", "expressive%3:00:00:communicative:00", "<NONE>", "<NONE>", "label%1:10:01", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "3", "4", "5", "<NONE>", "6", "<NONE>", "<NONE>", "8", "10", "<NONE>", "<NONE>", "12", "<NONE>", "<NONE>", "16", "<NONE>" ]
[ "<NONE>", "0.304", "<NONE>", "0.229", "0.42", "0.242", "<NONE>", "0.356", "<NONE>", "<NONE>", "0.377", "0.400", "<NONE>", "<NONE>", "0.465", "<NONE>", "<NONE>", "0.585", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
It is natural from the marksman 's viewpoint to call a bull's-eye a success , but in the mice example it is arbitrary which category corresponds to straight hair in a mouse .
<NONE>
<NONE>
[ "Il", "est", "naturel", ",", "du", "point", "de", "vue", "du", "tireur", "@-@", "tireur", ",", "d&apos;", "appeler", "un", "succès", "de", "l&apos;", "oeil", "de", "bullbys", ",", "mais", "dans", "l&apos;", "exemple", "des", "souris", "il", "est", "arbit...
[ "<NONE>", "be%2:42:03::", "natural%3:00:01::", "<NONE>", "<NONE>", "<NONE>", "viewpoint%1:09:00::", "<NONE>", "<NONE>", "marksman%1:18:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "call%2:32:00::", "<NONE>", "success%1:11:00::", "<NONE>", "bull's_eye%1:04:00::", "...
[ "<NONE>", "be%2:42:03", "natural%3:00:01", "<NONE>", "<NONE>", "<NONE>", "viewpoint%1:09:00", "<NONE>", "<NONE>", "marksman%1:18:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "call%2:32:00", "<NONE>", "success%1:11:00", "<NONE>", "bull's_eye%1:04:00", "<NONE>", "bu...
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br-j19
The word `` binomial '' means `` of two names '' or `` of two terms '' , and both usages apply in our work: the first to the names of the two outcomes of a binomial trial , and the second to the terms p and * * f that represent the probabilities of `` success '' and `` failure '' .
<NONE>
<NONE>
[ "Le", "mot", "&quot;", "rythme", "binomial", "&quot;", "signifie", "&quot;", "à", "deux", "noms", "&quot;", "ou", "&quot;", "à", "deux", "termes", "&quot;", ",", "et", "les", "deux", "usages", "s&apos;", "appliquent", "dans", "notre", "travail", ":", "le", ...
[ "<NONE>", "word%1:10:00::", "<NONE>", "<NONE>", "binomial%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "usage%1:04:00::", "<NONE>", ...
[ "<NONE>", "word%1:10:00", "<NONE>", "<NONE>", "binomial%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "usage%1:04:00", "<NONE>", "appl...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Sometimes when there are many outcomes for a single trial , we group these outcomes into two classes , as in the example of the die , where we have arbitrarily constructed the classes `` ace '' and `` not ace '' .
<NONE>
<NONE>
[ "Parfois", ",", "lorsqu&apos;", "il", "y", "a", "beaucoup", "de", "résultats", "pour", "un", "seul", "essai", ",", "nous", "regroupons", "ces", "résultats", "en", "deux", "catégories", ",", "comme", "dans", "l&apos;", "exemple", "de", "la", "mort", ",", "o...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:04::", "many%3:00:00::", "<NONE>", "outcome%1:11:00::", "<NONE>", "<NONE>", "single%3:00:00::", "trial%1:04:00::", "<NONE>", "<NONE>", "group%2:31:00::", "<NONE>", "outcome%1:11:00::", "<NONE>", "two%3:00:00:cardinal:00...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:04", "many%3:00:00", "<NONE>", "outcome%1:11:00", "<NONE>", "<NONE>", "single%3:00:00", "trial%1:04:00", "<NONE>", "<NONE>", "group%2:31:00", "<NONE>", "outcome%1:11:00", "<NONE>", "two%3:00:00:cardinal:00", "class%1:...
[ "<NONE>", "<NONE>", "1", "<NONE>", "2", "3", "4", "<NONE>", "5", "<NONE>", "6", "8", "9", "<NONE>", "11", "12", "13", "14", "15", "16", "17", "<NONE>", "19", "<NONE>", "20", "22", "<NONE>", "<NONE>", "25", "<NONE>", "27", "<NONE>", "29", "<NONE>", ...
[ "<NONE>", "<NONE>", "0.244", "<NONE>", "0.129", "0.122", "0.216", "<NONE>", "0.271", "<NONE>", "0.185", "0.244", "0.236", "<NONE>", "0.182", "0.227", "0.180", "0.258", "0.170", "0.229", "0.221", "<NONE>", "0.228", "<NONE>", "0.216", "0.242", "<NONE>", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
We classify mice as `` straight haired '' or `` wavy haired '' , but a hairless mouse appears .
<NONE>
<NONE>
[ "Nous", "classifions", "les", "souris", "comme", "du", "type", "&quot;", "à", "poils", "droits", "&quot;", "ou", "&quot;", "à", "poils", "&quot;", ",", "mais", "une", "souris", "sans", "poils", "apparaît", "." ]
[ "<NONE>", "classify%2:31:00::", "<NONE>", "mouse%1:05:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "haired%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "mouse%1:05:00::", "<NONE>", "hairless%3:...
[ "<NONE>", "classify%2:31:00", "<NONE>", "mouse%1:05:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "haired%3:00:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "mouse%1:05:00", "<NONE>", "hairless%3:00:00", ...
[ "<NONE>", "1", "<NONE>", "2", "3", "<NONE>", "<NONE>", "<NONE>", "4", "6", "<NONE>", "7", "<NONE>", "<NONE>", "9", "<NONE>", "<NONE>", "12", "14", "<NONE>", "17", "<NONE>", "16", "18", "<NONE>" ]
[ "<NONE>", "0.253", "<NONE>", "0.387", "0.175", "<NONE>", "<NONE>", "<NONE>", "0.343", "0.165", "<NONE>", "0.208", "<NONE>", "<NONE>", "0.407", "<NONE>", "<NONE>", "0.249", "0.226", "<NONE>", "0.251", "<NONE>", "0.399", "0.349", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
We can escape from such a difficulty by ruling out the animal as not constituting a trial , but such a solution is not always satisfactory .
<NONE>
<NONE>
[ "Nous", "pouvons", "échapper", "à", "une", "telle", "difficulté", "en", "déclarant", "que", "l&apos;", "animal", "ne", "constitue", "pas", "un", "essai", ",", "mais", "une", "telle", "solution", "n&apos;", "est", "pas", "toujours", "satisfaisante", "." ]
[ "<NONE>", "<NONE>", "escape_from%2:38:00::", "<NONE>", "<NONE>", "such%3:00:00:much:00", "difficulty%1:09:02::", "<NONE>", "rule_out%2:42:00::", "rule_out%2:42:00::", "<NONE>", "animal%1:03:00::", "<NONE>", "<NONE>", "constitute%2:42:00::", "<NONE>", "trial%1:04:00::", "<NONE>", ...
[ "<NONE>", "<NONE>", "escape_from%2:38:00", "<NONE>", "<NONE>", "such%3:00:00:much:00", "difficulty%1:09:02", "<NONE>", "rule_out%2:42:00", "rule_out%2:42:00", "<NONE>", "animal%1:03:00", "<NONE>", "<NONE>", "constitute%2:42:00", "<NONE>", "trial%1:04:00", "<NONE>", "<NONE>", "<...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j19
Each die has probability * * f of producing an ace; the marksman has some probability p , perhaps 0.1 , of making a bull's-eye .
<NONE>
<NONE>
[ "Chaque", "dé", "a", "une", "probabilité", "*", "*", "f", "de", "produire", "un", "ace.", "le", "tireur", "a", "une", "certaine", "probabilité", "p", ",", "peut", "@-@", "être", "0,1", ",", "de", "faire", "un", "bullrythme", "." ]
[ "<NONE>", "die%1:06:00::", "<NONE>", "<NONE>", "probability%1:07:01::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "produce%2:36:02::", "<NONE>", "ace%1:23:00::", "<NONE>", "marksman%1:18:00::", "have%2:42:00::", "<NONE>", "some%3:00:00::", "probability%1:07:01::", "<NONE>", "<NON...
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[ "<NONE>", "1", "<NONE>", "<NONE>", "3", "4", "5", "6", "<NONE>", "8", "<NONE>", "10", "<NONE>", "12", "13", "<NONE>", "14", "15", "16", "<NONE>", "18", "<NONE>", "<NONE>", "19", "<NONE>", "21", "22", "<NONE>", "24", "<NONE>" ]
[ "<NONE>", "0.341", "<NONE>", "<NONE>", "0.285", "0.189", "0.240", "0.267", "<NONE>", "0.227", "<NONE>", "0.321", "<NONE>", "0.244", "0.194", "<NONE>", "0.290", "0.269", "0.302", "<NONE>", "0.286", "<NONE>", "<NONE>", "0.286", "<NONE>", "0.163", "0.234", "<NONE>"...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j19
Note that we need not know the value of p , for the experiment to be binomial .
<NONE>
<NONE>
[ "Notez", "que", "nous", "n&apos;", "avons", "pas", "besoin", "de", "connaître", "la", "valeur", "de", "p", ",", "pour", "que", "l&apos;", "expérience", "soit", "binomiale", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "know%2:31:01::", "<NONE>", "value%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "binomial%3:01:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "know%2:31:01", "<NONE>", "value%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00", "<NONE>", "binomial%3:01:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "2", "<NONE>", "<NONE>", "3", "<NONE>", "<NONE>", "5", "6", "7", "8", "9", "<NONE>", "11", "12", "<NONE>", "13", "<NONE>", "16", "<NONE>" ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
During a round of target practice the sun comes from behind a cloud and dazzles the marksman , lowering his chance of a bull's-eye .
<NONE>
<NONE>
[ "Au", "cours", "d&apos;", "un", "tour", "de", "pratique", "cible", ",", "le", "soleil", "vient", "de", "derrière", "un", "nuage", "et", "éblouit", "le", "tireur", ",", "abaissant", "sa", "chance", "d&apos;", "un", "bullrythme", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "round%1:28:01::", "<NONE>", "<NONE>", "target_practice%1:04:00::", "<NONE>", "<NONE>", "sun%1:17:00::", "come%2:38:00::", "<NONE>", "<NONE>", "<NONE>", "cloud%1:17:00::", "<NONE>", "dazzle%2:39:00::", "<NONE>", "marksman%1:18:00::", "<...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "round%1:28:01", "<NONE>", "<NONE>", "target_practice%1:04:00", "<NONE>", "<NONE>", "sun%1:17:00", "come%2:38:00", "<NONE>", "<NONE>", "<NONE>", "cloud%1:17:00", "<NONE>", "dazzle%2:39:00", "<NONE>", "marksman%1:18:00", "<NONE>", "low...
[ "<NONE>", "<NONE>", "<NONE>", "1", "2", "<NONE>", "<NONE>", "5", "<NONE>", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "<NONE>", "18", "<NONE>", "20", "21", "<NONE>", "23", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "0.153", "0.281", "<NONE>", "<NONE>", "0.279", "<NONE>", "0.211", "0.335", "0.191", "0.249", "0.262", "0.261", "0.394", "0.197", "0.229", "0.230", "0.226", "<NONE>", "0.417", "<NONE>", "0.246", "0.296", "<NONE>", "0.48", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j19
Strictly speaking , this means that the probability for each possible outcome of the experiment can be computed by multiplying together the probabilities of the possible outcomes of the single binomial trials .
<NONE>
<NONE>
[ "Strictement", "parlant", ",", "cela", "signifie", "que", "la", "probabilité", "de", "chaque", "issue", "possible", "de", "l&apos;", "expérience", "peut", "être", "calculée", "en", "multipliant", "les", "probabilités", "des", "résultats", "possibles", "des", "essa...
[ "strictly_speaking%4:02:00::", "strictly_speaking%4:02:00::", "<NONE>", "<NONE>", "mean%2:32:03::", "<NONE>", "<NONE>", "probability%1:07:01::", "<NONE>", "each%3:00:00:all:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "<NONE>", "compute%2:31:00::",...
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[ "0", "1", "2", "3", "4", "5", "<NONE>", "7", "8", "9", "<NONE>", "<NONE>", "12", "13", "14", "<NONE>", "16", "17", "<NONE>", "19", "20", "22", "23", "26", "25", "<NONE>", "<NONE>", "30", "29", "32" ]
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br-j19
Thus in the three dice example * * f , * * f , and the independence assumption implies that the probability that the three dice fall ace , not ace , ace in that order is (1 6) (5 6) (1 6).
<NONE>
<NONE>
[ "Ainsi", ",", "dans", "l&apos;", "exemple", "des", "trois", "dés", "*", "*", "f", ",", "*", "*", "f", ",", "et", "l&apos;", "hypothèse", "de", "l&apos;", "indépendance", "implique", "que", "la", "probabilité", "que", "les", "trois", "dés", "tombent", ","...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "example%1:09:00::", "<NONE>", "three%3:00:00:cardinal:00", "dice%1:06:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "assumption%1:10:00::", "<NONE>", "independenc...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "example%1:09:00", "<NONE>", "three%3:00:00:cardinal:00", "dice%1:06:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "assumption%1:10:00", "<NONE>", "independence%1:26...
[ "<NONE>", "<NONE>", "1", "<NONE>", "5", "<NONE>", "3", "4", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "<NONE>", "17", "<NONE>", "16", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "29", "30", "31", "32", "33", "34"...
[ "<NONE>", "<NONE>", "0.159", "<NONE>", "0.184", "<NONE>", "0.205", "0.195", "0.133", "0.179", "0.250", "0.195", "0.193", "0.204", "0.262", "0.165", "0.176", "0.171", "<NONE>", "0.260", "<NONE>", "0.305", "0.204", "0.280", "0.132", "0.247", "0.189", "0.142", "0...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Experimentally , we expect independence when the trials have nothing to do with one another .
<NONE>
<NONE>
[ "Expérimentalement", ",", "nous", "attendons", "l&apos;", "indépendance", "lorsque", "les", "procès", "n&apos;", "ont", "rien", "à", "voir", "les", "uns", "avec", "les", "autres", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "expect%2:31:00::", "<NONE>", "independence%1:26:00::", "<NONE>", "<NONE>", "trial%1:04:00::", "<NONE>", "have%2:40:00::", "nothing%1:23:00::", "<NONE>", "do%2:42:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "expect%2:31:00", "<NONE>", "independence%1:26:00", "<NONE>", "<NONE>", "trial%1:04:00", "<NONE>", "have%2:40:00", "nothing%1:23:00", "<NONE>", "do%2:42:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "1", "2", "3", "<NONE>", "4", "5", "<NONE>", "7", "<NONE>", "8", "9", "<NONE>", "11", "12", "14", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "0.178", "0.214", "0.357", "<NONE>", "0.482", "0.248", "<NONE>", "0.390", "<NONE>", "0.235", "0.199", "<NONE>", "0.272", "0.169", "0.184", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
A family of five plans to go together either to the beach or to the mountains , and a coin is tossed to decide .
<NONE>
<NONE>
[ "Une", "famille", "de", "cinq", "personnes", "a", "l&apos;", "intention", "de", "se", "rassembler", "sur", "la", "plage", "ou", "sur", "les", "montagnes", ",", "et", "une", "pièce", "de", "monnaie", "est", "jetée", "pour", "décider", "." ]
[ "<NONE>", "family%1:14:02::", "<NONE>", "five%3:00:00:cardinal:00", "<NONE>", "<NONE>", "plan%2:31:01::", "<NONE>", "<NONE>", "<NONE>", "together%4:02:10::", "<NONE>", "<NONE>", "beach%1:17:00::", "<NONE>", "<NONE>", "<NONE>", "mountain%1:17:00::", "<NONE>", "<NONE>", "<NONE>...
[ "<NONE>", "family%1:14:02", "<NONE>", "five%3:00:00:cardinal:00", "<NONE>", "<NONE>", "plan%2:31:01", "<NONE>", "<NONE>", "<NONE>", "together%4:02:10", "<NONE>", "<NONE>", "beach%1:17:00", "<NONE>", "<NONE>", "<NONE>", "mountain%1:17:00", "<NONE>", "<NONE>", "<NONE>", "<NON...
[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "<NONE>", "4", "<NONE>", "<NONE>", "<NONE>", "7", "<NONE>", "<NONE>", "11", "12", "13", "<NONE>", "15", "<NONE>", "17", "18", "<NONE>", "19", "<NONE>", "20", "21", "22", "23", "24" ]
[ "<NONE>", "0.274", "<NONE>", "0.348", "<NONE>", "<NONE>", "0.335", "<NONE>", "<NONE>", "<NONE>", "0.222", "<NONE>", "<NONE>", "0.326", "0.285", "0.157", "<NONE>", "0.422", "<NONE>", "0.212", "0.159", "<NONE>", "0.343", "<NONE>", "0.166", "0.199", "0.221", "0.321...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
We want to know the number of people going to the mountains .
<NONE>
<NONE>
[ "Nous", "voulons", "connaître", "le", "nombre", "de", "personnes", "qui", "se", "rendent", "dans", "les", "montagnes", "." ]
[ "<NONE>", "want%2:37:00::", "know%2:31:01::", "<NONE>", "number%1:07:00::", "<NONE>", "people%1:14:00::", "go_to%2:42:00::", "<NONE>", "<NONE>", "go_to%2:42:00::", "<NONE>", "mountain%1:17:00::", "<NONE>" ]
[ "<NONE>", "want%2:37:00", "know%2:31:01", "<NONE>", "number%1:07:00", "<NONE>", "people%1:14:00", "go_to%2:42:00", "<NONE>", "<NONE>", "go_to%2:42:00", "<NONE>", "mountain%1:17:00", "<NONE>" ]
[ "<NONE>", "1", "3", "<NONE>", "5", "<NONE>", "7", "8", "<NONE>", "<NONE>", "9", "<NONE>", "11", "<NONE>" ]
[ "<NONE>", "0.344", "0.241", "<NONE>", "0.380", "<NONE>", "0.300", "0.263", "<NONE>", "<NONE>", "0.291", "<NONE>", "0.487", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
When this experiment is viewed as composed of five binomial trials , one for each member of the family , the outcomes of the trials are obviously not independent .
<NONE>
<NONE>
[ "Lorsque", "cette", "expérience", "est", "considérée", "comme", "composée", "de", "cinq", "essais", "binomiaux", ",", "un", "pour", "chaque", "membre", "de", "la", "famille", ",", "les", "résultats", "des", "essais", "ne", "sont", "manifestement", "pas", "indé...
[ "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "view_as%2:31:00::", "<NONE>", "compose%2:42:00::", "<NONE>", "five%3:00:00:cardinal:00", "<NONE>", "trial%1:04:00::", "<NONE>", "one%3:00:00:cardinal:00", "<NONE>", "<NONE>", "member%1:18:00::", "<NONE>", "<NONE>", "family%1:...
[ "<NONE>", "<NONE>", "experiment%1:04:00", "<NONE>", "view_as%2:31:00", "<NONE>", "compose%2:42:00", "<NONE>", "five%3:00:00:cardinal:00", "<NONE>", "trial%1:04:00", "<NONE>", "one%3:00:00:cardinal:00", "<NONE>", "<NONE>", "member%1:18:00", "<NONE>", "<NONE>", "family%1:14:02", ...
[ "<NONE>", "1", "2", "<NONE>", "4", "<NONE>", "6", "7", "8", "<NONE>", "10", "11", "12", "<NONE>", "14", "15", "<NONE>", "<NONE>", "18", "<NONE>", "<NONE>", "21", "<NONE>", "24", "<NONE>", "27", "26", "<NONE>", "28", "<NONE>" ]
[ "<NONE>", "0.194", "0.307", "<NONE>", "0.216", "<NONE>", "0.197", "0.163", "0.277", "<NONE>", "0.276", "0.132", "0.218", "<NONE>", "0.233", "0.276", "<NONE>", "<NONE>", "0.257", "<NONE>", "<NONE>", "0.256", "<NONE>", "0.240", "<NONE>", "0.212", "0.288", "<NONE>"...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Indeed , the experiment is better viewed as consisting of one binomial trial for the entire family .
<NONE>
<NONE>
[ "En", "fait", ",", "l&apos;", "expérience", "est", "mieux", "perçue", "comme", "un", "essai", "binomial", "pour", "toute", "la", "famille", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "better%4:02:00::", "<NONE>", "view_as%2:31:00::", "<NONE>", "one%3:00:00:cardinal:00", "binomial%3:01:00::", "<NONE>", "<NONE>", "<NONE>", "family%1:14:02::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00", "<NONE>", "better%4:02:00", "<NONE>", "view_as%2:31:00", "<NONE>", "one%3:00:00:cardinal:00", "binomial%3:01:00", "<NONE>", "<NONE>", "<NONE>", "family%1:14:02", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "2", "3", "<NONE>", "5", "<NONE>", "7", "8", "10", "11", "<NONE>", "13", "<NONE>", "16", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "0.144", "0.311", "<NONE>", "0.279", "<NONE>", "0.253", "0.245", "0.255", "0.319", "<NONE>", "0.185", "<NONE>", "0.391", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The following is a less extreme example of dependence .
<NONE>
<NONE>
[ "Voici", "un", "exemple", "moins", "extrême", "de", "dépendance", "." ]
[ "following%3:00:01:succeeding:00", "<NONE>", "example%1:09:00::", "less%4:02:00::", "extreme%3:00:00:immoderate:00", "<NONE>", "dependence%1:26:00::", "<NONE>" ]
[ "following%3:00:01:succeeding:00", "<NONE>", "example%1:09:00", "less%4:02:00", "extreme%3:00:00:immoderate:00", "<NONE>", "dependence%1:26:00", "<NONE>" ]
[ "1", "<NONE>", "6", "4", "5", "<NONE>", "8", "<NONE>" ]
[ "0.317", "<NONE>", "0.281", "0.265", "0.379", "<NONE>", "0.421", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Consider couples visiting an art museum .
<NONE>
<NONE>
[ "Pensez", "aux", "couples", "qui", "visitent", "un", "musée", "d&apos;", "art." ]
[ "<NONE>", "<NONE>", "couple%1:14:00::", "<NONE>", "visit%2:41:02::", "<NONE>", "museum%1:06:00::", "<NONE>", "art%1:06:00::" ]
[ "<NONE>", "<NONE>", "couple%1:14:00", "<NONE>", "visit%2:41:02", "<NONE>", "museum%1:06:00", "<NONE>", "art%1:06:00" ]
[ "<NONE>", "<NONE>", "1", "<NONE>", "2", "3", "5", "<NONE>", "4" ]
[ "<NONE>", "<NONE>", "0.430", "<NONE>", "0.380", "0.268", "0.340", "<NONE>", "0.425" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Each person votes for one of a pair of pictures to receive a popular prize .
<NONE>
<NONE>
[ "Chaque", "personne", "vote", "pour", "une", "des", "deux", "photos", "pour", "recevoir", "un", "prix", "populaire", "." ]
[ "<NONE>", "person%1:03:00::", "vote%2:41:13::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "pair%1:14:01::", "picture%1:06:01::", "receive%2:40:00::", "<NONE>", "prize%1:21:00::", "popular%3:00:00:democratic:00", "<NONE>" ]
[ "<NONE>", "person%1:03:00", "vote%2:41:13", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "pair%1:14:01", "picture%1:06:01", "receive%2:40:00", "<NONE>", "prize%1:21:00", "popular%3:00:00:democratic:00", "<NONE>" ]
[ "<NONE>", "1", "2", "3", "<NONE>", "<NONE>", "<NONE>", "7", "9", "11", "12", "14", "13", "<NONE>" ]
[ "<NONE>", "0.239", "0.317", "0.294", "<NONE>", "<NONE>", "<NONE>", "0.265", "0.238", "0.247", "0.190", "0.249", "0.319", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Voting for one picture may be called `` success '' , for the other `` failure '' .
<NONE>
<NONE>
[ "Le", "vote", "pour", "une", "image", "peut", "être", "appelé", "&quot;", "de", "réussite", "&quot;", ",", "pour", "l&apos;", "autre", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "one%3:00:00:cardinal:00", "picture%1:06:01::", "<NONE>", "<NONE>", "call%2:32:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "other%3:00:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "one%3:00:00:cardinal:00", "picture%1:06:01", "<NONE>", "<NONE>", "call%2:32:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "other%3:00:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "1", "2", "3", "4", "5", "6", "<NONE>", "7", "<NONE>", "9", "<NONE>", "11", "<NONE>", "13", "14" ]
[ "<NONE>", "<NONE>", "0.225", "0.245", "0.265", "0.199", "0.251", "0.275", "<NONE>", "0.559", "<NONE>", "0.450", "<NONE>", "0.209", "<NONE>", "0.247", "0.365" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
An experiment consists of the voting of one couple , or two trials .
<NONE>
<NONE>
[ "Une", "expérience", "consiste", "à", "voter", "un", "couple", "ou", "deux", "essais", "." ]
[ "<NONE>", "experiment%1:04:00::", "<NONE>", "<NONE>", "voting%1:04:00::", "<NONE>", "couple%1:14:00::", "<NONE>", "two%3:00:00:cardinal:00", "trial%1:04:00::", "<NONE>" ]
[ "<NONE>", "experiment%1:04:00", "<NONE>", "<NONE>", "voting%1:04:00", "<NONE>", "couple%1:14:00", "<NONE>", "two%3:00:00:cardinal:00", "trial%1:04:00", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "2", "5", "<NONE>", "8", "10", "11", "12", "<NONE>" ]
[ "<NONE>", "0.411", "<NONE>", "0.248", "0.293", "<NONE>", "0.318", "0.231", "0.272", "0.326", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
In repetitions of the experiment from couple to couple , the votes of the two persons in a couple probably agree more often than independence would imply , because couples who visit the museum together are more likely to have similar tastes than are a random pair of people drawn from the entire population of visitors .
<NONE>
<NONE>
[ "Dans", "les", "répétitions", "de", "l&apos;", "expérience", "de", "couple", "à", "couple", ",", "les", "votes", "des", "deux", "personnes", "dans", "un", "couple", "probablement", "d&apos;", "accord", "plus", "souvent", "que", "l&apos;", "indépendance", "impliq...
[ "<NONE>", "<NONE>", "repetition%1:04:00::", "<NONE>", "<NONE>", "experiment%1:04:00::", "<NONE>", "couple%1:14:00::", "<NONE>", "couple%1:14:00::", "<NONE>", "<NONE>", "vote%1:04:00::", "<NONE>", "two%3:00:00:cardinal:00", "person%1:03:00::", "<NONE>", "<NONE>", "couple%1:14:00::...
[ "<NONE>", "<NONE>", "repetition%1:04:00", "<NONE>", "<NONE>", "experiment%1:04:00", "<NONE>", "couple%1:14:00", "<NONE>", "couple%1:14:00", "<NONE>", "<NONE>", "vote%1:04:00", "<NONE>", "two%3:00:00:cardinal:00", "person%1:03:00", "<NONE>", "<NONE>", "couple%1:14:00", "probably...
[ "<NONE>", "<NONE>", "1", "<NONE>", "2", "4", "<NONE>", "6", "7", "8", "9", "10", "11", "<NONE>", "14", "15", "<NONE>", "16", "18", "19", "20", "<NONE>", "21", "22", "23", "<NONE>", "24", "26", "27", "28", "<NONE>", "<NONE>", "29", "<NONE>", "31", ...
[ "<NONE>", "<NONE>", "0.174", "<NONE>", "0.150", "0.240", "<NONE>", "0.192", "0.198", "0.197", "0.180", "0.126", "0.224", "<NONE>", "0.189", "0.226", "<NONE>", "0.200", "0.248", "0.184", "0.254", "<NONE>", "0.172", "0.239", "0.179", "<NONE>", "0.284", "0.228", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Table 7 - 1 illustrates the point .
<NONE>
<NONE>
[ "Le", "tableau", "7", "@-@", "1", "illustre", "ce", "point", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "illustrate%2:32:00::", "<NONE>", "point%1:10:01::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "illustrate%2:32:00", "<NONE>", "point%1:10:01", "<NONE>" ]
[ "<NONE>", "<NONE>", "1", "2", "3", "4", "<NONE>", "6", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.318", "0.408", "0.331", "0.354", "<NONE>", "0.370", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The table shows that 0.6 of the boys and 0.6 of the girls vote for picture A .
<NONE>
<NONE>
[ "Le", "tableau", "montre", "que", "0,6", "des", "garçons", "et", "0,6", "des", "filles", "votent", "pour", "le", "tableau", "A." ]
[ "<NONE>", "table%1:14:00::", "show%2:39:02::", "<NONE>", "<NONE>", "<NONE>", "boy%1:18:00::", "<NONE>", "<NONE>", "<NONE>", "girl%1:18:02::", "vote%2:41:13::", "<NONE>", "<NONE>", "picture%1:06:01::", "<NONE>" ]
[ "<NONE>", "table%1:14:00", "show%2:39:02", "<NONE>", "<NONE>", "<NONE>", "boy%1:18:00", "<NONE>", "<NONE>", "<NONE>", "girl%1:18:02", "vote%2:41:13", "<NONE>", "<NONE>", "picture%1:06:01", "<NONE>" ]
[ "<NONE>", "1", "2", "<NONE>", "4", "<NONE>", "7", "8", "9", "<NONE>", "12", "13", "<NONE>", "<NONE>", "15", "16" ]
[ "<NONE>", "0.350", "0.261", "<NONE>", "0.313", "<NONE>", "0.318", "0.185", "0.364", "<NONE>", "0.319", "0.402", "<NONE>", "<NONE>", "0.411", "0.373" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Therefore , under independent voting , * * f or 0.36 of the couples would cast two votes for picture A , and * * f or 0.16 would cast two votes for picture B .
<NONE>
<NONE>
[ "Par", "conséquent", ",", "dans", "le", "cas", "d&apos;", "un", "vote", "indépendant", ",", "*", "*", "f", "ou", "0,36", "des", "couples", "voteraient", "pour", "la", "photo", "A", ",", "et", "*", "*", "f", "ou", "0,16", "pour", "la", "photo", "B", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "voting%1:04:00::", "independent%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "couple%1:14:00::", "<NONE>", "two%3:00:00:cardinal:00", "<NONE>", "picture%1:0...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "voting%1:04:00", "independent%3:00:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "couple%1:14:00", "<NONE>", "two%3:00:00:cardinal:00", "<NONE>", "picture%1:06:01",...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "2", "<NONE>", "<NONE>", "<NONE>", "4", "3", "<NONE>", "6", "7", "8", "9", "10", "<NONE>", "13", "14", "16", "<NONE>", "19", "20", "<NONE>", "22", "23", "24", "25", "26", "27", "<NONE>", "<NONE>", "33", "34", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.301", "<NONE>", "<NONE>", "<NONE>", "0.206", "0.290", "<NONE>", "0.187", "0.219", "0.303", "0.212", "0.257", "<NONE>", "0.270", "0.098", "0.174", "<NONE>", "0.298", "0.249", "<NONE>", "0.177", "0.174", "0.223", "0.280",...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Thus in independent voting , * * f or 0.52 of the couples would agree .
<NONE>
<NONE>
[ "Ainsi", ",", "dans", "le", "cas", "du", "vote", "indépendant", ",", "*", "*", "f", "ou", "0,52", "des", "couples", "seraient", "d&apos;", "accord", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "voting%1:04:00::", "independent%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "couple%1:14:00::", "<NONE>", "<NONE>", "agree%2:32:00::", "<NONE>" ]
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[ "<NONE>", "<NONE>", "<NONE>", "1", "<NONE>", "<NONE>", "3", "2", "<NONE>", "5", "6", "7", "<NONE>", "9", "<NONE>", "12", "<NONE>", "<NONE>", "14", "15" ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
But Table 7 - 1 shows that * * f or 0.70 agree , too many for independent voting .
<NONE>
<NONE>
[ "Mais", "le", "tableau", "7", "@-@", "1", "montre", "que", "*", "*", "f", "ou", "0,70", "sont", "d&apos;", "accord", ",", "trop", "pour", "le", "vote", "indépendant", "." ]
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[ "<NONE>", "<NONE>", "0.386", "0.282", "0.339", "0.299", "0.252", "0.279", "0.191", "0.229", "0.343", "0.239", "0.296", "<NONE>", "<NONE>", "0.366", "0.177", "0.248", "<NONE>", "0.334", "0.227", "0.354", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Each performance of an n-trial binomial experiment results in some whole number from 0 through n as the value of the random variable X , where * * f .
<NONE>
<NONE>
[ "Chaque", "performance", "d&apos;", "une", "expérience", "binomiale", "à", "l&apos;", "essai", "donne", "un", "nombre", "entier", "de", "0", "à", "n", "comme", "valeur", "de", "la", "variable", "aléatoire", "X", ",", "où", "*", "*", "f." ]
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[ "<NONE>", "0.225", "<NONE>", "<NONE>", "<NONE>", "0.303", "<NONE>", "<NONE>", "0.288", "0.197", "<NONE>", "0.184", "0.261", "0.179", "0.174", "0.323", "0.220", "0.220", "<NONE>", "0.170", "<NONE>", "0.247", "0.288", "0.301", "<NONE>", "0.337", "0.265", "0.255", ...
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br-j19
We want to study the probability function of this random variable .
<NONE>
<NONE>
[ "Nous", "voulons", "étudier", "la", "fonction", "de", "probabilité", "de", "cette", "variable", "aléatoire", "." ]
[ "<NONE>", "want%2:37:00::", "study%2:31:02::", "<NONE>", "function%1:24:00::", "probability%1:07:01::", "<NONE>", "<NONE>", "<NONE>", "random_variable%1:09:00::", "random_variable%1:09:00::", "<NONE>" ]
[ "<NONE>", "want%2:37:00", "study%2:31:02", "<NONE>", "function%1:24:00", "probability%1:07:01", "<NONE>", "<NONE>", "<NONE>", "random_variable%1:09:00", "random_variable%1:09:00", "<NONE>" ]
[ "<NONE>", "1", "3", "<NONE>", "6", "5", "<NONE>", "<NONE>", "8", "10", "9", "<NONE>" ]
[ "<NONE>", "0.369", "0.314", "<NONE>", "0.344", "0.441", "<NONE>", "<NONE>", "0.300", "0.279", "0.428", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
For example , we are interested in the number of bull's-eyes , not which shots were bull's-eyes .
<NONE>
<NONE>
[ "Par", "exemple", ",", "nous", "sommes", "intéressés", "par", "le", "nombre", "de", "bullaucs-yeux", ",", "pas", "quels", "tirs", "ont", "été", "bullheures", "s-", "yeux", "." ]
[ "<NONE>", "for_example%4:02:00::", "<NONE>", "<NONE>", "<NONE>", "interested%3:00:00::", "<NONE>", "<NONE>", "number%1:07:00::", "<NONE>", "bull's_eye%1:04:00::", "<NONE>", "not%4:02:00::", "<NONE>", "shot%1:04:00::", "<NONE>", "be%2:42:06::", "bull's_eye%1:04:00::", "bull's_eye%...
[ "<NONE>", "for_example%4:02:00", "<NONE>", "<NONE>", "<NONE>", "interested%3:00:00", "<NONE>", "<NONE>", "number%1:07:00", "<NONE>", "bull's_eye%1:04:00", "<NONE>", "not%4:02:00", "<NONE>", "shot%1:04:00", "<NONE>", "be%2:42:06", "bull's_eye%1:04:00", "bull's_eye%1:04:00", "bul...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
A binomial experiment can produce random variables other than the number of successes .
<NONE>
<NONE>
[ "Une", "expérience", "binomiale", "peut", "produire", "des", "variables", "aléatoires", "autres", "que", "le", "nombre", "de", "succès", "." ]
[ "<NONE>", "experiment%1:04:00::", "binomial%3:01:00::", "<NONE>", "produce%2:36:02::", "<NONE>", "random_variable%1:09:00::", "random_variable%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "number%1:07:00::", "<NONE>", "success%1:11:00::", "<NONE>" ]
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[ "<NONE>", "2", "1", "3", "4", "<NONE>", "6", "5", "7", "8", "9", "10", "<NONE>", "12", "<NONE>" ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
For example , the marksman gets 5 shots , but we take his score to be the number of shots before his first bull's-eye , that is , 0 , 1 , 2 , 3 , 4 (or 5 , if he gets no bull's-eye).
<NONE>
<NONE>
[ "Par", "exemple", ",", "le", "tireur", "obtient", "5", "coups", "de", "feu", ",", "mais", "nous", "prenons", "son", "score", "comme", "le", "nombre", "de", "tirs", "avant", "son", "premier", "bullrythme", "s-eye", ",", "c&apos;", "est", "@-@", "à", "@-@"...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j19
Thus we do not score the number of bull's-eyes , and the random variable is not the number of successes .
<NONE>
<NONE>
[ "Par", "conséquent", ",", "nous", "ne", "cotons", "pas", "le", "nombre", "de", "bullheures", "@-@", "yeux", ",", "et", "la", "variable", "aléatoire", "n&apos;", "est", "pas", "le", "nombre", "de", "succès", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "not%4:02:00::", "score%2:32:00::", "<NONE>", "<NONE>", "number%1:07:00::", "<NONE>", "bull's_eye%1:04:00::", "<NONE>", "bull's_eye%1:04:00::", "<NONE>", "<NONE>", "<NONE>", "random_variable%1:09:00::", "random_variable%1:09:00::", "<NONE>"...
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[ "<NONE>", "<NONE>", "<NONE>", "0.173", "0.168", "0.258", "<NONE>", "0.163", "0.295", "<NONE>", "0.507", "<NONE>", "0.285", "<NONE>", "0.256", "<NONE>", "0.236", "0.340", "<NONE>", "0.250", "0.196", "0.184", "0.343", "<NONE>", "0.345", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The constancy of p and the independence are the conditions most likely to give trouble in practice .
<NONE>
<NONE>
[ "La", "constance", "de", "p", "et", "l&apos;", "indépendance", "sont", "les", "conditions", "les", "plus", "susceptibles", "de", "causer", "des", "problèmes", "dans", "la", "pratique", "." ]
[ "<NONE>", "constancy%1:07:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "independence%1:26:00::", "be%2:42:06::", "<NONE>", "condition%1:10:01::", "<NONE>", "most%4:02:01::", "likely%3:00:00::", "give%2:40:03::", "<NONE>", "<NONE>", "trouble%1:09:00::", "<NONE>", "<NONE>", "in...
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[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "4", "6", "7", "<NONE>", "9", "<NONE>", "10", "11", "13", "<NONE>", "<NONE>", "14", "<NONE>", "<NONE>", "16", "<NONE>" ]
[ "<NONE>", "0.320", "<NONE>", "0.302", "<NONE>", "0.233", "0.372", "0.212", "<NONE>", "0.266", "<NONE>", "0.245", "0.229", "0.179", "<NONE>", "<NONE>", "0.431", "<NONE>", "<NONE>", "0.468", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
Obviously , very slight changes in p do not change the probabilities much , and a slight lack of independence may not make an appreciable difference .
<NONE>
<NONE>
[ "De", "toute", "évidence", ",", "de", "très", "légères", "variations", "de", "p", "ne", "modifient", "pas", "beaucoup", "les", "probabilités", ",", "et", "un", "léger", "manque", "d&apos;", "indépendance", "peut", "ne", "pas", "faire", "une", "différence", "...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
(For instance , see Example 2 of Section 5 - 5 , on red cards in hands of 5 .)
<NONE>
<NONE>
[ "Voir", "par", "exemple", "l&apos;", "exemple", "2", "de", "la", "section", "5", "-", "5", ",", "sur", "les", "cartes", "rouges", "entre", "les", "mains", "de", "5", ".", ")" ]
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
On the other hand , even when the binomial model does not describe well the physical phenomenon being studied , the binomial model may still be used as a baseline for comparative purposes; that is , we may discuss the phenomenon in terms of its departures from the binomial model .
<NONE>
<NONE>
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br-j19
A binomial experiment consists of * * f independent binomial trials , all with the same probability * * f of yielding a success .
<NONE>
<NONE>
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br-j19
The outcome of the experiment is X successes .
<NONE>
<NONE>
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br-j19
The random variable X takes the values * * f with probabilities * * f or , more briefly * * f .
<NONE>
<NONE>
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br-j19
We shall find a formula for the probability of exactly x successes for given values of p and n .
<NONE>
<NONE>
[ "Nous", "allons", "trouver", "une", "formule", "pour", "la", "probabilité", "de", "succès", "x", "exacts", "pour", "des", "valeurs", "données", "de", "p", "et", "n." ]
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br-j19
When each number of successes x is paired with its probability of occurrence * * f , the set of pairs * * f , is a probability function called a binomial distribution .
<NONE>
<NONE>
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br-j19
The choice of p and n determines the binomial distribution uniquely , and different choices always produce different distributions (except when * * f; then the number of successes is always 0).
<NONE>
<NONE>
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br-j19
The set of all binomial distributions is called the family of binomial distributions , but in general discussions this expression is often shortened to `` the binomial distribution '' , or even `` the binomial '' when the context is clear .
<NONE>
<NONE>
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br-j19
Binomial distributions were treated by James Bernoulli about 1700 , and for this reason binomial trials are sometimes called Bernoulli trials .
<NONE>
<NONE>
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br-j19
Each binomial trial of a binomial experiment produces either 0 or 1 success .
<NONE>
<NONE>
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br-j19
Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1 , with probabilities q and p respectively .
<NONE>
<NONE>
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br-j19
The several trials of a binomial experiment produce a new random variable X , the total number of successes , which is just the sum of the random variables associated with the single trials .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
The marksman gets two bull's-eyes , one on his third shot and one on his fifth .
<NONE>
<NONE>
[ "Le", "tireur", "obtient", "deux", "bulllocs", "@-@", "yeux", ",", "l&apos;", "un", "sur", "son", "troisième", "et", "l&apos;", "autre", "sur", "son", "cinquième", "." ]
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[ "<NONE>", "marksman%1:18:00", "get%2:40:01", "two%3:00:00:cardinal:00", "bull's_eye%1:04:00", "<NONE>", "bull's_eye%1:04:00", "<NONE>", "<NONE>", "one%3:00:00:cardinal:00", "<NONE>", "<NONE>", "third%3:00:00:ordinal:00", "shot%1:04:00", "<NONE>", "one%3:00:00:cardinal:00", "<NONE>", ...
[ "<NONE>", "1", "2", "3", "4", "<NONE>", "4", "5", "<NONE>", "6", "7", "8", "9", "10", "<NONE>", "12", "13", "14", "15", "<NONE>" ]
[ "<NONE>", "0.254", "0.199", "0.245", "0.568", "<NONE>", "0.310", "0.155", "<NONE>", "0.299", "0.177", "0.206", "0.253", "0.288", "<NONE>", "0.248", "0.214", "0.223", "0.316", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The numbers of successes on the five individual shots are , then , 0 , 0 , 1 , 0 , 1 .
<NONE>
<NONE>
[ "Les", "nombres", "de", "succès", "sur", "les", "cinq", "plans", "individuels", "sont", "donc", ",", "0", ",", "0", ",", "1", ",", "0", ",", "1", "." ]
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[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "4", "6", "<NONE>", "8", "9", "11", "<NONE>", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22" ]
[ "<NONE>", "0.279", "<NONE>", "0.313", "<NONE>", "0.187", "0.262", "<NONE>", "0.201", "0.198", "0.264", "<NONE>", "0.201", "0.213", "0.282", "0.224", "0.275", "0.186", "0.279", "0.246", "0.296", "0.288" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j19
The number of successes on each shot is a value of a random variable that has values 0 or 1 , and there are 5 such random variables here .
<NONE>
<NONE>
[ "Le", "nombre", "de", "succès", "sur", "chaque", "photo", "est", "une", "valeur", "d&apos;", "une", "variable", "aléatoire", "qui", "a", "des", "valeurs", "0", "ou", "1", ",", "et", "il", "ya", "5", "telles", "variables", "aléatoires", "ici", "." ]
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[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "5", "6", "<NONE>", "8", "9", "<NONE>", "11", "13", "12", "<NONE>", "15", "<NONE>", "16", "17", "18", "19", "<NONE>", "21", "<NONE>", "22", "24", "25", "<NONE>", "26", "28", "29" ]
[ "<NONE>", "0.260", "<NONE>", "0.291", "<NONE>", "0.206", "0.342", "<NONE>", "0.168", "0.267", "<NONE>", "0.176", "0.218", "0.281", "<NONE>", "0.215", "<NONE>", "0.354", "0.283", "0.312", "0.242", "<NONE>", "0.214", "<NONE>", "0.231", "0.192", "0.237", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j19
Their sum is X , the total number of successes , which in this experiment has the value * * f .
<NONE>
<NONE>
[ "Leur", "somme", "est", "X", ",", "le", "nombre", "total", "de", "succès", "qui", ",", "dans", "cette", "expérience", ",", "a", "la", "valeur", "*", "*", "f." ]
[ "<NONE>", "sum%1:09:01::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "total%3:00:00:whole:00", "<NONE>", "success%1:11:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00::", "have%2:42:00::", "<NONE>", "<NONE>", "value%1:09:00::", "<NONE>", "<NONE>", ...
[ "<NONE>", "sum%1:09:01", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "total%3:00:00:whole:00", "<NONE>", "success%1:11:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "experiment%1:04:00", "have%2:42:00", "<NONE>", "<NONE>", "value%1:09:00", "<NONE>", "<NONE>", "<NONE>" ...
[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "5", "<NONE>", "6", "<NONE>", "9", "<NONE>", "<NONE>", "12", "13", "14", "15", "<NONE>", "<NONE>", "17", "18", "19", "20" ]
[ "<NONE>", "0.344", "<NONE>", "0.286", "<NONE>", "0.196", "<NONE>", "0.287", "<NONE>", "0.353", "<NONE>", "<NONE>", "0.241", "0.249", "0.373", "0.261", "<NONE>", "<NONE>", "0.286", "0.236", "0.285", "0.322" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
Consider a simple , closed , plane curve C which is a real analytic image of the unit circle , and which is given by **f .
<NONE>
<NONE>
[ "Considérez", "une", "courbe", "plane", "C", "simple", "et", "fermée", ",", "qui", "est", "une", "image", "analytique", "réelle", "du", "cercle", "de", "l&apos;", "unité", ",", "et", "qui", "est", "donnée", "par", "le", "système", "." ]
[ "<NONE>", "<NONE>", "simple%3:00:02::", "curve%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "closed%3:00:02::", "<NONE>", "<NONE>", "be%2:42:03::", "<NONE>", "real%3:00:00::", "image%1:06:00::", "<NONE>", "<NONE>", "<NONE>", "circle%1:25:00::", "<NONE>", "unit%1:09:00::", "<NONE...
[ "<NONE>", "<NONE>", "simple%3:00:02", "curve%1:25:00", "<NONE>", "<NONE>", "<NONE>", "closed%3:00:02", "<NONE>", "<NONE>", "be%2:42:03", "<NONE>", "real%3:00:00", "image%1:06:00", "<NONE>", "<NONE>", "<NONE>", "circle%1:25:00", "<NONE>", "unit%1:09:00", "<NONE>", "<NONE>", ...
[ "<NONE>", "<NONE>", "2", "7", "8", "<NONE>", "<NONE>", "4", "<NONE>", "9", "10", "<NONE>", "12", "14", "<NONE>", "<NONE>", "<NONE>", "18", "<NONE>", "17", "<NONE>", "20", "<NONE>", "22", "23", "24", "<NONE>", "<NONE>", "25" ]
[ "<NONE>", "<NONE>", "0.171", "0.274", "0.196", "<NONE>", "<NONE>", "0.267", "<NONE>", "0.211", "0.180", "<NONE>", "0.235", "0.212", "<NONE>", "<NONE>", "<NONE>", "0.243", "<NONE>", "0.319", "<NONE>", "0.183", "<NONE>", "0.167", "0.258", "0.284", "<NONE>", "<NONE...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
These are real analytic periodic functions with period T .
<NONE>
<NONE>
[ "Ce", "sont", "de", "vraies", "fonctions", "analytiques", "périodiques", "avec", "la", "période", "T", "." ]
[ "<NONE>", "be%2:42:03::", "<NONE>", "real%3:00:00::", "function%1:24:00::", "analytic%3:01:00::", "periodic%3:00:00::", "<NONE>", "<NONE>", "period%1:28:00::", "<NONE>", "<NONE>" ]
[ "<NONE>", "be%2:42:03", "<NONE>", "real%3:00:00", "function%1:24:00", "analytic%3:01:00", "periodic%3:00:00", "<NONE>", "<NONE>", "period%1:28:00", "<NONE>", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "2", "5", "3", "4", "6", "<NONE>", "7", "8", "<NONE>" ]
[ "<NONE>", "0.376", "<NONE>", "0.459", "0.270", "0.336", "0.378", "0.238", "<NONE>", "0.441", "0.408", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
In the following paper it is shown that in a certain definite sense , exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares .
<NONE>
<NONE>
[ "Dans", "le", "présent", "article", ",", "il", "est", "montré", "que", "dans", "un", "certain", "sens", "précis", ",", "exactement", "un", "nombre", "impair", "de", "carrés", "peut", "être", "inscrit", "dans", "chaque", "courbe", "qui", "ne", "contient", "...
[ "<NONE>", "<NONE>", "<NONE>", "paper%1:10:00::", "<NONE>", "<NONE>", "<NONE>", "show%2:31:00::", "<NONE>", "<NONE>", "<NONE>", "certain%3:00:00:definite:00", "<NONE>", "definite%3:00:00::", "<NONE>", "exactly%4:02:01::", "<NONE>", "<NONE>", "odd%3:00:00::", "<NONE>", "square%...
[ "<NONE>", "<NONE>", "<NONE>", "paper%1:10:00", "<NONE>", "<NONE>", "<NONE>", "show%2:31:00", "<NONE>", "<NONE>", "<NONE>", "certain%3:00:00:definite:00", "<NONE>", "definite%3:00:00", "<NONE>", "exactly%4:02:01", "<NONE>", "<NONE>", "odd%3:00:00", "<NONE>", "square%1:25:00", ...
[ "<NONE>", "<NONE>", "<NONE>", "3", "<NONE>", "<NONE>", "<NONE>", "6", "<NONE>", "8", "12", "10", "<NONE>", "11", "13", "14", "15", "<NONE>", "16", "18", "19", "20", "<NONE>", "22", "23", "24", "25", "<NONE>", "27", "<NONE>", "30", "<NONE>", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "0.319", "<NONE>", "<NONE>", "<NONE>", "0.235", "<NONE>", "0.151", "0.185", "0.198", "<NONE>", "0.253", "0.205", "0.210", "0.186", "<NONE>", "0.205", "0.143", "0.160", "0.206", "<NONE>", "0.251", "0.207", "0.210", "0.235", "<NONE>",...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed , bounded convex set in **f .
<NONE>
<NONE>
[ "Ce", "théorème", "est", "similaire", "au", "théorème", "de", "Kakutani", "qu&apos;", "il", "existe", "un", "cube", "de", "circoncision", "autour", "de", "n&apos;", "importe", "quel", "ensemble", "convexe", "fermé", "et", "limité", "dans", "le", "domaine", "de...
[ "<NONE>", "theorem%1:10:00::", "<NONE>", "similar%3:00:00::", "<NONE>", "theorem%1:10:00::", "<NONE>", "person%1:03:00::", "<NONE>", "<NONE>", "<NONE>", "exist%2:42:00::", "cube%1:25:00::", "<NONE>", "circumscribe%2:35:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", ...
[ "<NONE>", "theorem%1:10:00", "<NONE>", "similar%3:00:00", "<NONE>", "theorem%1:10:00", "<NONE>", "person%1:03:00", "<NONE>", "<NONE>", "<NONE>", "exist%2:42:00", "cube%1:25:00", "<NONE>", "circumscribe%2:35:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "c...
[ "<NONE>", "1", "<NONE>", "3", "4", "6", "<NONE>", "8", "9", "<NONE>", "<NONE>", "11", "14", "<NONE>", "13", "15", "<NONE>", "<NONE>", "16", "<NONE>", "<NONE>", "20", "19", "17", "18", "<NONE>", "<NONE>", "23", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "0.538", "<NONE>", "0.292", "0.168", "0.415", "<NONE>", "0.284", "0.232", "<NONE>", "<NONE>", "0.209", "0.373", "<NONE>", "0.254", "0.237", "<NONE>", "<NONE>", "0.349", "<NONE>", "<NONE>", "0.294", "0.199", "0.182", "0.175", "<NONE>", "<NONE>", "0.532"...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
The latter theorem has been generalized by Yamabe and Yujobo , and Cairns to show that in **f there are families of such cubes .
<NONE>
<NONE>
[ "Ce", "dernier", "théorème", "a", "été", "généralisé", "par", "Yamabe", "et", "Yujobo", ",", "et", "Cairns", "pour", "montrer", "qu&apos;", "il", "y", "a", "des", "familles", "de", "tels", "cubes", "dans", "le", "domaine", "du", "développement", "." ]
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[ "<NONE>", "1", "2", "<NONE>", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "<NONE>", "19", "<NONE>", "20", "<NONE>", "22", "23", "<NONE>", "<NONE>", "<NONE>", "17", "<NONE>", "<NONE>" ]
[ "<NONE>", "0.239", "0.539", "<NONE>", "0.170", "0.255", "0.243", "0.35", "0.237", "0.273", "0.179", "0.241", "0.295", "0.245", "0.264", "0.269", "0.178", "<NONE>", "0.219", "<NONE>", "0.314", "<NONE>", "0.248", "0.261", "<NONE>", "<NONE>", "<NONE>", "0.530", "...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
Here , for the case of squares inscribed in plane curves , we remove the restriction to convexity and give certain other results .
<NONE>
<NONE>
[ "Ici", ",", "pour", "le", "cas", "des", "carrés", "inscrits", "dans", "les", "courbes", "planes", ",", "nous", "supprimons", "la", "restriction", "à", "la", "convexité", "et", "donnons", "certains", "autres", "résultats", "." ]
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[ "<NONE>", "<NONE>", "<NONE>", "0.214", "0.257", "0.220", "0.184", "0.310", "0.259", "<NONE>", "0.342", "0.326", "0.169", "0.233", "0.288", "0.188", "0.292", "<NONE>", "<NONE>", "0.362", "0.215", "0.281", "0.240", "0.292", "0.268", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
A square inscribed in a curve C means a square with its four corner points on the curve , though it may not lie entirely in the interior of C .
<NONE>
<NONE>
[ "Un", "carré", "inscrit", "dans", "une", "courbe", "C", "désigne", "un", "carré", "dont", "les", "quatre", "pointes", "sont", "sur", "la", "courbe", ",", "bien", "qu&apos;", "il", "ne", "puisse", "pas", "se", "trouver", "entièrement", "à", "l&apos;", "inté...
[ "<NONE>", "square%1:25:00::", "inscribed%3:00:00:written:00", "<NONE>", "<NONE>", "curve%1:25:00::", "<NONE>", "<NONE>", "mean%2:32:03::", "square%1:25:00::", "<NONE>", "<NONE>", "four%3:00:00:cardinal:00", "point%1:09:00::", "corner%1:15:00::", "<NONE>", "<NONE>", "curve%1:25:00::...
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[ "<NONE>", "1", "2", "<NONE>", "3", "5", "<NONE>", "<NONE>", "7", "9", "<NONE>", "10", "12", "14", "13", "15", "<NONE>", "17", "<NONE>", "<NONE>", "19", "<NONE>", "21", "22", "<NONE>", "<NONE>", "23", "24", "25", "<NONE>", "27", "<NONE>", "29", "<NONE...
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br-j20
Indeed , the spiral **f , with the two endpoints connected by a straight line possesses only one inscribed square .
<NONE>
<NONE>
[ "En", "effet", ",", "la", "spirale", "du", "rythme", ",", "avec", "les", "deux", "extrémités", "connectées", "par", "une", "ligne", "droite", ",", "ne", "possède", "qu&apos;", "une", "seule", "place", "inscrite", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "spiral%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "two%3:00:00:cardinal:00", "endpoint%1:15:00::", "connected%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "straight_line%1:25:00::", "<NONE>", "possess%2:42:00::", "<NONE>"...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "spiral%1:25:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "two%3:00:00:cardinal:00", "endpoint%1:15:00", "connected%3:00:00", "<NONE>", "<NONE>", "<NONE>", "straight_line%1:25:00", "<NONE>", "possess%2:42:00", "<NONE>", "<NONE...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "3", "<NONE>", "4", "4", "6", "<NONE>", "8", "9", "10", "11", "12", "<NONE>", "13", "<NONE>", "15", "<NONE>", "<NONE>", "16", "17", "<NONE>", "18", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.224", "<NONE>", "0.461", "0.389", "0.218", "<NONE>", "0.258", "0.273", "0.300", "0.288", "0.213", "<NONE>", "0.368", "<NONE>", "0.276", "<NONE>", "<NONE>", "0.234", "0.230", "<NONE>", "0.364", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
The square has one corner point on the straight line segment , and does not lie entirely in the interior .
<NONE>
<NONE>
[ "Le", "carré", "a", "un", "point", "d&apos;", "angle", "sur", "le", "segment", "de", "ligne", "droite", "et", "ne", "se", "trouve", "pas", "entièrement", "à", "l&apos;", "intérieur", "." ]
[ "<NONE>", "square%1:25:00::", "<NONE>", "have%2:42:00::", "one%3:00:00:cardinal:00", "corner%1:15:00::", "<NONE>", "<NONE>", "<NONE>", "segment%1:06:00::", "<NONE>", "<NONE>", "straight_line%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "lie%2:42:00::", "<NONE>", "entirely%4:02:00::"...
[ "<NONE>", "square%1:25:00", "<NONE>", "have%2:42:00", "one%3:00:00:cardinal:00", "corner%1:15:00", "<NONE>", "<NONE>", "<NONE>", "segment%1:06:00", "<NONE>", "<NONE>", "straight_line%1:25:00", "<NONE>", "<NONE>", "<NONE>", "lie%2:42:00", "<NONE>", "entirely%4:02:00", "<NONE>", ...
[ "<NONE>", "1", "<NONE>", "2", "3", "4", "<NONE>", "<NONE>", "6", "10", "<NONE>", "<NONE>", "8", "<NONE>", "13", "<NONE>", "15", "<NONE>", "16", "17", "<NONE>", "19", "<NONE>" ]
[ "<NONE>", "0.316", "<NONE>", "0.225", "0.280", "0.365", "<NONE>", "<NONE>", "0.178", "0.248", "<NONE>", "<NONE>", "0.385", "<NONE>", "0.158", "<NONE>", "0.237", "<NONE>", "0.339", "0.199", "<NONE>", "0.420", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
On C , from the point P at **f to the point Q at **f , we construct the chord , and upon the chord as a side erect a square in such a way that as s approaches zero the square is inside C .
<NONE>
<NONE>
[ "Sur", "C", ",", "du", "point", "P", "à", "la", "chaîne", ",", "jusqu&apos;", "au", "point", "Q", "au", "niveau", "du", "jour", ",", "nous", "construisons", "la", "corde", ",", "et", "sur", "la", "corde", "comme", "côté", "ériger", "une", "place", "d...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "point%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "point%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "construct%2:35:00::", "<NONE>", "chord%1:25:00::", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "point%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "point%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "construct%2:35:00", "<NONE>", "chord%1:25:00", "chord%1...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
As s increases we consider the two free corner points of the square , **f and **f , adjacent to P and Q respectively .
<NONE>
<NONE>
[ "À", "mesure", "que", "s", "s", "augmente", ",", "nous", "considérons", "les", "deux", "points", "de", "coin", "libre", "du", "carré", ",", "le", "taux", "de", "rendement", "et", "le", "taux", "de", "rendement", ",", "adjacents", "à", "P", "et", "Q", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "increase%2:30:00::", "<NONE>", "<NONE>", "consider%2:31:01::", "<NONE>", "two%3:00:00:cardinal:00", "<NONE>", "corner%1:15:00::", "<NONE>", "free%3:00:00::", "<NONE>", "square%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
As s approaches T the square will be outside C and therefore both **f and **f must cross C an odd number of times as s varies from zero to T .
<NONE>
<NONE>
[ "À", "l&apos;", "approche", "de", "T", ",", "le", "carré", "sera", "à", "l&apos;", "extérieur", "de", "C", "et", ",", "par", "conséquent", ",", "les", "deux", "systèmes", "doivent", "traverser", "C", "un", "nombre", "impair", "de", "fois", ",", "car", ...
[ "<NONE>", "<NONE>", "approach%2:38:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "square%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "outside%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "therefore%4:02:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE...
[ "<NONE>", "<NONE>", "approach%2:38:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "square%1:25:00", "<NONE>", "<NONE>", "<NONE>", "outside%3:00:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "therefore%4:02:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "c...
[ "<NONE>", "<NONE>", "2", "<NONE>", "3", "4", "<NONE>", "5", "<NONE>", "<NONE>", "<NONE>", "8", "9", "<NONE>", "10", "<NONE>", "<NONE>", "11", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "13", "17", "18", "19", "<NONE>", "20", "<NONE>", "23", "<NONE>", "24", ...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j20
The points may also touch C without crossing .
<NONE>
<NONE>
[ "Les", "points", "peuvent", "aussi", "toucher", "C", "sans", "traverser", "." ]
[ "<NONE>", "point%1:09:00::", "<NONE>", "also%4:02:00::", "touch%2:35:01::", "<NONE>", "<NONE>", "cross%2:38:03::", "<NONE>" ]
[ "<NONE>", "point%1:09:00", "<NONE>", "also%4:02:00", "touch%2:35:01", "<NONE>", "<NONE>", "cross%2:38:03", "<NONE>" ]
[ "<NONE>", "1", "<NONE>", "3", "4", "5", "6", "7", "<NONE>" ]
[ "<NONE>", "0.405", "<NONE>", "0.353", "0.410", "0.415", "0.436", "0.454", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
Suppose **f crosses C when **f .
<NONE>
<NONE>
[ "Supposons", "des", "croisements", "de", "type", "&quot;", "à", "la", "carte", "&quot;", "C", "lorsque", "le", "logiciel", "est", "utilisé", "." ]
[ "suppose%2:32:00::", "<NONE>", "cross%2:38:03::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "suppose%2:32:00", "<NONE>", "cross%2:38:03", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "0", "<NONE>", "2", "<NONE>", "<NONE>", "<NONE>", "1", "<NONE>", "<NONE>", "<NONE>", "3", "4", "<NONE>", "<NONE>", "5", "<NONE>", "5" ]
[ "0.376", "<NONE>", "0.349", "<NONE>", "<NONE>", "<NONE>", "0.540", "<NONE>", "<NONE>", "<NONE>", "0.225", "0.271", "<NONE>", "<NONE>", "0.556", "<NONE>", "0.236" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
We now have certain squares with three corners on C .
<NONE>
<NONE>
[ "Nous", "avons", "maintenant", "certaines", "places", "avec", "trois", "coins", "sur", "C", "." ]
[ "<NONE>", "<NONE>", "now%4:02:00::", "certain%3:00:00:definite:00", "square%1:25:00::", "<NONE>", "three%3:00:00:cardinal:00", "corner%1:15:00::", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "now%4:02:00", "certain%3:00:00:definite:00", "square%1:25:00", "<NONE>", "three%3:00:00:cardinal:00", "corner%1:15:00", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "1", "3", "4", "5", "6", "7", "8", "9", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.272", "0.261", "0.215", "0.279", "0.266", "0.267", "0.209", "0.384", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square .
<NONE>
<NONE>
[ "Pour", "un", "tel", "carré", ",", "le", "coin", "médian", "sera", "appelé", "le", "vertex", "du", "carré", "et", "le", "coin", "non", "sur", "la", "courbe", "sera", "appelé", "le", "point", "diagonal", "du", "carré", "." ]
[ "<NONE>", "<NONE>", "such%3:00:00:much:00", "square%1:25:00::", "<NONE>", "<NONE>", "<NONE>", "middle%3:00:01:central:01", "<NONE>", "call%2:32:02::", "<NONE>", "vertex%1:09:00::", "<NONE>", "square%1:25:00::", "<NONE>", "<NONE>", "corner%1:15:00::", "not%4:02:00::", "<NONE>", ...
[ "<NONE>", "<NONE>", "such%3:00:00:much:00", "square%1:25:00", "<NONE>", "<NONE>", "<NONE>", "middle%3:00:01:central:01", "<NONE>", "call%2:32:02", "<NONE>", "vertex%1:09:00", "<NONE>", "square%1:25:00", "<NONE>", "<NONE>", "corner%1:15:00", "not%4:02:00", "<NONE>", "<NONE>", ...
[ "<NONE>", "1", "2", "3", "<NONE>", "4", "<NONE>", "5", "<NONE>", "11", "12", "13", "<NONE>", "16", "<NONE>", "17", "19", "20", "21", "<NONE>", "23", "<NONE>", "26", "27", "29", "28", "30", "32", "<NONE>" ]
[ "<NONE>", "0.224", "0.222", "0.288", "<NONE>", "0.165", "<NONE>", "0.178", "<NONE>", "0.219", "0.181", "0.313", "<NONE>", "0.260", "<NONE>", "0.207", "0.262", "0.274", "0.248", "<NONE>", "0.274", "<NONE>", "0.287", "0.212", "0.199", "0.299", "0.213", "0.276", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j20
Each point on C , as a vertex , may possess a finite number of corresponding diagonal points by the above construction .
<NONE>
<NONE>
[ "Chaque", "point", "de", "C", ",", "en", "tant", "que", "vertex", ",", "peut", "avoir", "un", "nombre", "fini", "de", "points", "diagonaux", "correspondants", "par", "la", "construction", "ci", "@-@", "dessus", "." ]
[ "<NONE>", "point%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "vertex%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "possess%2:42:00::", "number%1:23:00::", "finite%3:00:00::", "<NONE>", "point%1:09:00::", "diagonal%3:00:02:oblique:00", "corresponding%3:00:...
[ "<NONE>", "point%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "vertex%1:09:00", "<NONE>", "<NONE>", "<NONE>", "possess%2:42:00", "number%1:23:00", "finite%3:00:00", "<NONE>", "point%1:09:00", "diagonal%3:00:02:oblique:00", "corresponding%3:00:00:similar:0...
[ "<NONE>", "1", "2", "3", "<NONE>", "<NONE>", "5", "<NONE>", "7", "<NONE>", "9", "<NONE>", "10", "13", "12", "<NONE>", "17", "16", "15", "<NONE>", "18", "21", "<NONE>", "20", "<NONE>", "<NONE>" ]
[ "<NONE>", "0.271", "0.224", "0.222", "<NONE>", "<NONE>", "0.348", "<NONE>", "0.347", "<NONE>", "0.264", "<NONE>", "0.213", "0.220", "0.218", "<NONE>", "0.221", "0.266", "0.292", "<NONE>", "0.201", "0.291", "<NONE>", "0.311", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j20
To each paired vertex and diagonal point there corresponds a unique forward corner point , i.e. , the corner on C reached first by proceeding along C from the vertex in the direction of increasing t .
<NONE>
<NONE>
[ "Pour", "chaque", "point", "vertex", "et", "point", "diagonal", "apparié", ",", "il", "y", "a", "un", "point", "d&apos;", "intersection", "unique", "vers", "l&apos;", "avant", ",", "c&apos;", "est", "@-@", "à", "@-@", "dire", "que", "le", "coin", "de", "...
[ "<NONE>", "<NONE>", "<NONE>", "vertex%1:09:00::", "<NONE>", "<NONE>", "diagonal%3:00:02:oblique:00", "paired%3:00:00:matched:00", "<NONE>", "<NONE>", "correspond%2:42:04::", "<NONE>", "<NONE>", "unique%3:00:00:single:05", "corner%1:15:00::", "<NONE>", "<NONE>", "<NONE>", "forward...
[ "<NONE>", "<NONE>", "<NONE>", "vertex%1:09:00", "<NONE>", "<NONE>", "diagonal%3:00:02:oblique:00", "paired%3:00:00:matched:00", "<NONE>", "<NONE>", "correspond%2:42:04", "<NONE>", "<NONE>", "unique%3:00:00:single:05", "corner%1:15:00", "<NONE>", "<NONE>", "<NONE>", "forward%3:00:...
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br-j20
If the vertex is at **f , and if the interior of C is on the left as one moves in the direction of increasing t , then every such corner can be found from the curve obtained by rotating C clockwise through 90 ` about the vertex .
<NONE>
<NONE>
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