context stringlengths 545 71.9k | questionsrc stringlengths 16 10.2k | question stringlengths 11 563 |
|---|---|---|
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | why is the vertical axis denoted p ( x ) , when the corresponding point on this axis to the x-axis does n't denote a probability ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | my question is , if you 're looking for p ( y=2 ) and you use the area between 1.9 and 2.1 , are n't those arbitrary numbers ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | why not look for the area under the pdf between say , 1.95 and 2.05 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | you could also say what 's the probability we have less than 0.1 of rain ? then you would go here and if this was 0.1 , you would calculate this area . and you could say what 's the probability that we have more than 4 inches of rain tomorrow ? | the former would give smaller value , the latter a larger , so why pick those boundaries ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | for the graph that sal draws beginning what does the y axis represent ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and hopefully that 's not an infinite number , right ? then your probability wo n't make any sense . but hopefully if you take this sum it comes to some number . | i understand how the probability of the event is represented by the area under the curve , but does n't that mean the y axis does n't chart probability , but something different ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and let 's say i do n't know what the actual probability distribution function for this is , but i 'll draw one and then we 'll interpret it . just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density fun... | this might be a stupid question , but is a probability distribution function related only to discrete random variables and a probability density function is for continuous random variables ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | and what label should be for the vertical axis ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | can someone explain to me how 0 p ( ly-2l < .1 ) is the same as p ( 1.9 < y < 2.1 ) ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | what is the unit of the values on the y-axis ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and hopefully that 's not an infinite number , right ? then your probability wo n't make any sense . but hopefully if you take this sum it comes to some number . | which makes sense when you are talking about area under a curve , but it does n't make intuitive sense because does n't that mean that the probability of anything happening in a continuous variable is zero ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | we 've been having a drought , so that 's a good thing . but the exact amount of rain tomorrow . and let 's say i do n't know what the actual probability distribution function for this is , but i 'll draw one and then we 'll interpret it . | so if it rains in california , the exact amount of rain that came down had a zero probability of happening ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and it should make intuitive sense . that the probability of a very super-exact thing happening is pretty much 0 . that you really have to say , ok what 's the probably that we 'll get close to 2 ? | why is probability of an exact value = 0 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | what is the probability of 5 out of 25 saw blades will be defective ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and the these , i was going to say that they tend to be integers , but they do n't always have to be integers . you have discrete , so finite meaning you ca n't have an infinite number of values for a discrete random variable . and then we have the continuous , which can take on an infinite number . | is the probability of a given value of a discrete random variable zero if the discrete random variable has countably infinite possibilities ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and before we even think about how we would interpret it visually , let 's just think about it logically . what is the probability that tomorrow we have exactly 2 inches of rain ? not 2.01 inches of rain , not 1.99 inches of rain . | what is the probability of having exactly four heads out of 19 coin flips ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | how would you show that on a probability density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and all of this should immediately lead to one light bulb in your head , is that the probability of all of the events that might occur ca n't be more than 100 % . right ? all the events combined -- there 's a probability of 1 that one of these events will occur . | that is , if there really is a 10 % chance it does n't rain at all , the height of the pdf at x=0 would infinite , right ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | if half of a spinner was labeled `` 3 '' and the other half had a smooth gradient of numbers from 5 to 10 , would this be a discrete or continuous variable or some combination of the two types ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and people do tend to use -- let me change it a little bit , just so you can see it can be something other than an x . let 's have the random variable capital y . they do tend to be capital letters . | does the random variable need to map to every possible random value that can be obtained ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | could i define my random variable x to be 1 if 1 faces up 2 if 2 faces up 3 if 3 faces up 4 if 4 faces up 5 if 5 faces up but then not define any value for x if 6 faces up ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | how would find the probability of having no rain in his continuous probability density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | what is the difference between probability density function and binomial distribution ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . | what about questions such as : determine x such that p ( x < x ) = .1 or p ( x < = x ) = .1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | what is the probability that the amount of rain would be between 1.9 and 2.1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | why do we find the area under the function to find its probability ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's a very important thing to realize . because when a random variable can take on an infinite number of values , or it can take on any value between an interval , to get an exact value , to get exactly 1.999 , the probability is actually 0 . it 's like asking you what is the area under a curve on just this line . | can the random variable take negative value in any case ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | you 'd say it looks like it 's about 0.5 . and you 'd say , i do n't know , is it a 0.5 chance ? and i would say no , it is not a 0.5 chance . and before we even think about how we would interpret it visually , let 's just think about it logically . | a die is rolled four times.what is the chance that all the rolls show 3ormore spots ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so from -- let me see , i 've run out of space down here . so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . | why is the graph not supporting what sal is claiming ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | p ( y = 2 ) is 0 , then in the graph why is f ( 2 ) not equal to 0 and is equal to 0.5 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and all of this should immediately lead to one light bulb in your head , is that the probability of all of the events that might occur ca n't be more than 100 % . right ? all the events combined -- there 's a probability of 1 that one of these events will occur . | therefore the graph 's value for all points should be zero right ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and area is key . so if you want to know the probability of this occurring , you actually want the area under this curve from this point to this point . and for those of you who have studied your calculus , that would essentially be the definite integral of this probability density function from this point to this poin... | if y axis represents the probability value at a point ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . and area is key . so if you want to know the probability of this occurring , you actually want the area under this curve from this point to this point . | what is the `` y axis '' then defined as if the area under the function is the prob ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and you can watch the calculus videos if you want to learn a little bit more about how to do them . and this also applies to the discrete probability distributions . let me draw one . | extending from discrete variables , their probability was not the area under the graph but rather just the corresponding value on the y-axis , why should it be any different here ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | it would be all of this kind of stuff . you could also say what 's the probability we have less than 0.1 of rain ? then you would go here and if this was 0.1 , you would calculate this area . and you could say what 's the probability that we have more than 4 inches of rain tomorrow ? | i can intuitively see why any 1 value would have the probability of 0 , but even then , where does the area under the graph come in ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | what is the y axis here.. frequency or prabibility ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and all of this should immediately lead to one light bulb in your head , is that the probability of all of the events that might occur ca n't be more than 100 % . right ? all the events combined -- there 's a probability of 1 that one of these events will occur . | after all , the curve depicts the probabilities at each point on the x-axis , right ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | what 's the probability of that happening ? well , based on how we thought about the probability distribution functions for the discrete random variable , you 'd say ok , let 's see . 2 inches , that 's the case we care about right now . | where is the video for probability density functions for discrete random variables ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | or even more specifically , it 's like asking you what 's the area of a line ? an area of a line , if you were to just draw a line , you 'd say well , area is height times base . well the height has some dimension , but the base , what 's the width the a line ? | can you calculate he area under a wavy distribution as well ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . | of a day suitable for re-roofing is what ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is th... | i understand that we have to consider interval , but should n't probability be just length of interval part of the f ( x ) , that small curve of f ( x ) values that correspond to 1.9 - 2.1 x interval ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and then we have the continuous , which can take on an infinite number . and the example i gave for continuous is , let 's say random variable x . and people do tend to use -- let me change it a little bit , just so you can see it can be something other than an x . | will this case be considered continuous or discrete random variable ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | where the probability function comes from ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | because then you would have essentially 120 % probability of either of the outcomes happening , which makes no sense at all . so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . | is it true that the probability function of a continuous random variable is the counterpart to the probability mass function of a discrete random variable ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and the example i gave for continuous is , let 's say random variable x . and people do tend to use -- let me change it a little bit , just so you can see it can be something other than an x . let 's have the random variable capital y . | what sorts of techniques do statisticians use to create pdfs ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the way you would think about a continuous random variable , you could say what is the probability that y is almost 2 ? so if we said that the absolute value of y minus is 2 is less than some tolerance ? is less than 0.1 . | why would the absolute value of y minus 2 be less than 1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | 1.99 does not count . normally our measurements , we do n't even have tools that can tell us whether it is exactly 2 inches . no ruler you can even say is exactly 2 inches long . | can you please tell the derivation of empirical rule ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and let 's say i do n't know what the actual probability distribution function for this is , but i 'll draw one and then we 'll interpret it . just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density fun... | is there an intuitive way to think about the values of the pdf ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . | so i totally understand how the probability of an exact value of x is zero , but then what is f ( x ) ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | where do i access the video on probability density function of discrete random variables ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so if we said that the absolute value of y minus is 2 is less than some tolerance ? is less than 0.1 . and if that does n't make sense to you , this is essentially just saying what is the probability that y is greater than 1.9 and less than 2.1 ? | a computer generates independent random numbers from the continuous uniform distribution over the range ( 0,1 ) in a sample of 6 such number , what is the probability that exactly 2 are less than 0.39 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so if we said that the absolute value of y minus is 2 is less than some tolerance ? is less than 0.1 . and if that does n't make sense to you , this is essentially just saying what is the probability that y is greater than 1.9 and less than 2.1 ? | just a general question : from this video , can we conclude 1/infinity = 0 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | can somebody explain to me , what does normdist ( x , mean , probability,0 ) give in excel ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | it might not be obvious to you , because you 've probably heard , oh , we had 2 inches of rain last night . but think about it , exactly 2 inches , right ? normally if it 's 2.01 people will say that 's 2 . but we 're saying no , this does not count . | what is the y axis represent ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so if we said that the absolute value of y minus is 2 is less than some tolerance ? is less than 0.1 . and if that does n't make sense to you , this is essentially just saying what is the probability that y is greater than 1.9 and less than 2.1 ? | is n't integral of f ( x ) on the interval where it is defined ( in our case from 0 to inf ) always 1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and the these , i was going to say that they tend to be integers , but they do n't always have to be integers . you have discrete , so finite meaning you ca n't have an infinite number of values for a discrete random variable . and then we have the continuous , which can take on an infinite number . | why ca n't discrete random variables take infinite values ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . | why is not the probability of it to be nearly 2 '' = ( integral of f ( x ) dx from 1.99 to 2.01 ) or ( integral of f ( x ) dx from 1.9 to 2.1 ) / ( integral of f ( x ) dx from 0 to infinity ) ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | 0 , is .5 a bad example for the height ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | if the y axis is not probability of a particular rainfall level , what is it ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and if you said oh , what 's the probability that we get someplace between 1 and 3 inches of rain , then of course the probability is much higher . the probability is much higher . it would be all of this kind of stuff . | would n't the probability of there being no rain be higher than 0 , if you think about it logically ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and this also applies to the discrete probability distributions . let me draw one . the sum of all of the probabilities have to be equal to 1 . | what is a type one error ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and all of this should immediately lead to one light bulb in your head , is that the probability of all of the events that might occur ca n't be more than 100 % . right ? all the events combined -- there 's a probability of 1 that one of these events will occur . | so if i am asking the possibility of |y-2| < 0.1 , i am actually asking the possibility of a continuous random variable right ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | why we use density and mass words in terms `` probability mass function '' and `` probability density function '' ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | can you explain to me briefly how you would calculate the probability that 1.9 < = y < = 2.1 if the probability that 1.9 < y < 2.1 is the integral of f ( x ) from 1.9 to 2.1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . and area is key . so if you want to know the probability of this occurring , you actually want the area under this curve from this point to this point . | why do we take area as measurement of probability ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | what is the difference between a probability distribution function and a probability density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and people do tend to use -- let me change it a little bit , just so you can see it can be something other than an x . let 's have the random variable capital y . they do tend to be capital letters . | is it valid under all conditions ( independent of the type of random variable ) ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and then you can define an area . and if you said oh , what 's the probability that we get someplace between 1 and 3 inches of rain , then of course the probability is much higher . the probability is much higher . | what is the probability that in a batch of 10 players , 3 would be defective ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and the these , i was going to say that they tend to be integers , but they do n't always have to be integers . you have discrete , so finite meaning you ca n't have an infinite number of values for a discrete random variable . and then we have the continuous , which can take on an infinite number . | can someone give me an example when is there a probability of a discrete random variable with an irrational number ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | we 've been having a drought , so that 's a good thing . but the exact amount of rain tomorrow . and let 's say i do n't know what the actual probability distribution function for this is , but i 'll draw one and then we 'll interpret it . | so y , exact amount of rain is continuous ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . | should practical f ( x ) tend to infinitive when x tends to zero ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | how do we get a probability distribution function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | what are the things we get on the x and y axis of pdf ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | i 'm not sure if i missed something during the video , but is the graph that sal drew a graph of a probability function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . assuming this is the x-axis . so it 's a very important thing to realize . | 8 , if the x-axis is inches , and later on it is shown that the area under the curve is the probability , what is the y-axis representative of , as far as units or meaning ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | understand from the video that probability distribution and probability density are the same but please explain what is the difference between probability distribution and relative frequency ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | and let 's say i do n't know what the actual probability distribution function for this is , but i 'll draw one and then we 'll interpret it . just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density fun... | do you simply have to think of the probability as an event within a range of values ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | they do tend to be capital letters . is equal to the exact amount of rain tomorrow . and i say rain because i 'm in northern california . | however , how continuous distribution functions are constructed , where probability of the exact level of rain for example is equal to zero ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | where this is 0 inches , this is 1 inch , this is 2 inches , this is 3 inches , 4 inches . and then this is some height . let 's say it peaks out here at , i do n't know , let 's say this 0.5 . | what is the height ( y axis ) ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | why is the probability density function used in economics ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | why does sal use shorthand notation ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | not 1.99999 inches of rain , not 2.000001 inches of rain . exactly 2 inches of rain . i mean , there 's not a single extra atom , water molecule above the 2 inch mark . | the probability of exactly 2 inches of rain isnt exactly 0 right ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | not 1.99999 inches of rain , not 2.000001 inches of rain . exactly 2 inches of rain . i mean , there 's not a single extra atom , water molecule above the 2 inch mark . | there is an infitely small chance of there being 2 inches of rain up to the electron scale ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | hi , my question might not be valid also ... but i got thinking if he says we are going to take area between the 1.9 to 2.1 but how can be any one be sure about there also be uncertainty about 1.9 and 2.1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so it 's important to realize that a probability distribution function , in this case for a discrete random variable , they all have to add up to 1 . so 0.5 plus 0.5 . and in this case the area under the probability density function also has to be equal to 1 . | what is the probability of 5 out of 25 saw blades will be defective ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | so , the curve is in fact the density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | now we have an interval here . so we want all y 's between 1.9 and 2.1 . so we are now talking about this whole area . | and to get the probability of 1.9-2.1 '' rain tomorrow is the integral from 1.9 to 2.1 ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | if not , what is the density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | just so you can kind of think about how you can think about continuous random variables . so let me draw a probability distribution , or they call it its probability density function . and we draw like this . | do you have an example of finding the .95 quantile of a density function ? |
in the last video , i introduced you to the notion of -- well , really we started with the random variable . and then we moved on to the two types of random variables . you had discrete , that took on a finite number of values . and the these , i was going to say that they tend to be integers , but they do n't always h... | so let 's say if this graph -- let me draw it in a different color . if this line was defined by , i 'll call it f of x. i could call it p of x or something . the probability of this happening would be equal to the integral , for those of you who 've studied calculus , from 1.9 to 2.1 of f of x dx . | such that p ( y < phi sub.95 ) = .95 ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | statement number two , `` an unbalanced force on a body will always impact the object 's speed . '' also an interesting statement . statement number three , `` the reason why initially moving objects tend to come to rest in our everyday life is because they are being acted on by unbalanced forces . '' | for statement # 3 , does light also apply ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | an unbalanced force on a body will always impact the object 's velocity . that would be true . but we wrote `` speed '' here . | if you attempt to move an object and you applupy exactly thensame amount of force as friction would apply , what exactly would happen ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . | would the object move just a little bit ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | an unbalanced force on an object will not always change the object 's direction . it can , like these circumstances , but not always . so `` always '' is what makes this very , very , very wrong . | my teacher says that objects like the moon are in free fall , but why does it stay put and just rotate around the earth ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | an unbalanced force on an object will not always change the object 's direction . it can , like these circumstances , but not always . so `` always '' is what makes this very , very , very wrong . | is it like a vacuum or is it just the gravity is stronger than the free fall ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | so this is not true . an unbalanced force on an object will not always change the object 's direction . it can , like these circumstances , but not always . | if an object experiences a net zero external unbalanced force , is it possible for the object to be travelling with a non zero velocity ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | that would be true . but we wrote `` speed '' here . speed is the magnitude of velocity . it does not take into account the direction . | what is the difference between speed and velocity ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | so the force , the inward force , the tension from the rope pulling on the skater in this situation , would have only changed the skater 's direction . so and unbalanced force does n't necessarily have to impact the object 's speed . it often does . | so how in the world does n't an unbalanced force change the speed ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | so if that is some type of planet , and this is one of the planet 's moons right over here , the reason why it stays in orbit is because the pull of gravity keeps making the object change its direction , but not its speed . its speed is the exact right speed . so this was its speed right here . | 5 , sal says if it was velocity instead of speed , statment 02 would be right..i donot get.does anyone please explain ? |
now that we know a little bit about newton 's first law , let 's give ourselves a little quiz . and what i want you to do is figure out which of these statements are actually true . and our first statement is , `` if the net force on a body is zero , its velocity will not change . '' interesting . statement number two ... | so this is not true . an unbalanced force on an object will not always change the object 's direction . it can , like these circumstances , but not always . | does an object have tiny hills and valleys , and is the connection of a valley and a mountain the force of friction ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.