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10 55 ABABBAA, ABABABA, ABABAAB, ABAABBA,
ABAABAB, ABAAABB, AABBBAA, AABBABA,
AABBAAB, AABABBA, AABABAB, AABAABB,
71. a. Mode = .93. It occurs four times in the data set. ‘AAABBBA. AAABBAB, AAABABB, AAAABBB)
b. The Modal Category is the one in which the most b. (AAAABBB, AAABABB, AAABBAB, AABAABB,
observations occur. AABABAB}
73. The measures that are sensitive to outliers are the mean 13, a, 07 b..30. ¢..57
and the midrange. The mean is sensitive because all -
values are used in computing it, The midrange is the 15. a. They are awarded at least one of the first two projects,
most sensitive because it uses only the most extreme 36.
values in its computation, b. They are awarded neither of the first two projects, .64.
‘The median, the trimmed mean, and the midfourth are ¢. They are awarded at least one of the projects, .53.
less sensitive to outliers. The median is the most resistant d. They are awarded none of the projects, .47.
to outliers because it uses only the middle value (or e, They are awarded only the third project, .17.
values) in its computation. The midfourth is also quite f, Either they fail to get the first two or they are awarded
resistant because it uses the fourths. The resistance of the the third, .75.
trimmed mean increases with the trimming percentage. 47 4 579, 879
Tet bl POS S8s bake aad 19. a. SAS and SPSS ate not the only packages.
77. b. 552, .102 30 d.19 b.7 8 d.2
79. a. There may be a tendency to a repeating pattern. 21. a. 8841 b, .0435
b. The value .1 gives a much smoother series. ,
©. The smoothed value depends on all previous values of 2° % 10 b- 18,19 41 4.59 €.31 £69
the time series, but the coefficient decreases withk. 25, a, 1/15 b.6/15. @ 14/15. 8/15
d. As fgets large, the coefficient (1 — «)'"' decreases to
zero, so there is decreasing sensitivity to the initial 27- a. 98 b..02 ¢..03. d..24
value; 29.2. 1/9 b.8/9 €.2/9
31. a. 20 b.60 © 10
Chapter 2 33. a. 243 b. 3645, 10
1. a, ANB! b. AUB ¢. (ANB') U (BNA') 35. .0679
3. a. S = (1324, 1342, 1423, 1432, 2314, 2341, 2413, 37, 2
2431, 3124, 3142, 4123, 4132, 3214, 3241,
4213, 4231) 39. 0456
b. A = (1324, 1342, 1423, 1432}
c. B= (2314, 2341, 2413, 2431, 3214, 3241, 4213, AA Ja O89 BuL2AOTS &.21998
4231} 43. a. 1/15 b.1B ©2238
d. AUB = (1324, 1342, 1423, 1432, 2314, 2341, 2413,
2431, 3214, 3241, 4213, 4231) 45. a. 447, (5,2
ADB = @ b. P(AIC) = 4, the fraction of ethnic group C that has
A’ = (2314, 2341, 2413, 2431, 3124, 3142, 4123, blood type A.
4132, 3214, 3241, 4213, 4231} P(CIA) = .447, the fraction of those with blood group
A that are of ethnic group C.
5. a. A= [ SSF, SFS, FSS } e211
b. B = | SSS, SSF, SFS, FSS }
¢. C = { SSS, SSF, SFS } 47. a. Of those with a Visa card, .5 is the proportion who also
d. C’ =| SFF, FSS, FSF, FFS, FFF } have a Master Card.
‘AUC = { SSS, SSF, SES, FSS } b. Of those with a Visa card, .5 is the proportion who do
‘ANC = | SSE, SFS } not have a Master Card.
BUC = { SSS, SSF, SFS, FSS }
BNC = { SSS SSF, SFS }
--- Trang 831 ---
818 Chapter 3
¢. Of those with Master Card, .625 is the proportion
who also have a Visa Card. Chapter 3
d. OF those with Master Card, .375 is the proportion
who do not have a Visa Card. “Ss: FFF SFF FSF FFS FSS SFS SSF SSS
e. Of those with at least one of the two cards, .769 is the x £ 4 i 2 2, 2: a
proportion who have a Visa card.
do BER AR 3. M = the absolute value of the difference between the
alte outcomes, with possible values 0, 1, 2, 3, 4, 5 or 6;
51. 436, 582 W = Lif the sum of the two resulting numbers is even
and W = 0 otherwise, a Bemoulli random variable.
53. .0833
5. No, X can be a Bemoulli random variable where a
59. a, 067 b. 509 success is an outcome in B, with B a particular subset
x, (287 of the sample space.
7 7. a. Possible values are 0, 1,2, ..., 12; discrete
SS BGS Bie2A5 b. With N = # on the list, values are 0, 1,2, ..., Ns
65. 466, .288, .247 discrete
¢. Possible values are 1, 2, 3,4, ... ; discrete
67. a. Because of independence, the conditional probability d. (.x:0 <x < 00 } if we assume that a rattlesnake can
is the same as the unconditional probability, .3. be arbitrarily short or long; not discrete
b. 82 ¢. 146 e. With c = amount earned per book sold, possible
. rm values are 0, ¢, 2c, 3c, ... , 10,000¢; discrete
TAs 349,,651; 1 — py — py f. { y: 0 < y < 14} since 0 is the smallest possible pH
73. 99999969, 226 and 14 is the largest possible pH; not discrete
g. With m and M denoting the minimum and maximum
75. .9981 possible tension, respectively, possible values are {
a 8 x:m <x <M }; not discrete
+ Sessny, h. Possible values are 3, 6, 9, 12, 15, ... —ie., 3(1),
79. a. 2p—p? b1-(—p)" a(l—py 3(2), 3(3), 3(4), .. giving a first element, etc,; discrete
3
dis Seas] <p) veni013e 9. a. X isa discrete random variable with possible values
81. .8588, 9896 {2, 4, 6,8...
b. X is a discrete random variable with possible values
83. 2n(1 — 2) {2, 3,4, 5,...}
85. a. 1/3,.444 b..1S e291 II. a. p(4) = 10. 45, .25
87. 45,32 13. a. 70 b.45 6.55 d71 e.65 £45
89. a. 1/120 b. 1/5 © 1/5 45. a. (1,2) (1,3) (1,4) (1,5) (2.3) (2,4) (2,5) (3,4) (3,5) (4,5)
a BONE b. pO) = 3, pl) = 6, p2) = 1, p(x) = 0 otherwise
- ¢. F(O) = .30, F(1) = .90, F(2) = 1. The c.d.f. is
93. a. 904 b. .766 0 x<0
F(a) =) 30 OS x<1
95. .008 @)=4 90 1<x<2
97. .362, 348, .290 1 28x
99. a. P(GIR, < Ry < Rs) = 2/3, so classify as granite if 17. a. 81 b. .162
Ry < Re < Re ¢, The fifth battery must be an A, and one of the first
b. P(GIR, < Ry < Ry) = .294, so classify as basalt if four must also be an A, so
Ri < Ry < Ry pS) = P(AUUUA or UAUUA or UUAUA or