Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 18
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20Answers
9.
(a) There are 2 possible sequences.
n
(b) The number containing exactly j “lefts” is
.
j
n
(c) P(X = j) =
2 .
j
(d) With n = 6 the distribution of X is
j
0
1
2
3
4
5
6
P(X = j) 0.015625 0.09375 0.234375 0.3125 0.234375 0.09375 0.015625
10. Let Y be the number of the first defective item.
P(X = j)
P(Y = 13 X = j)
P(Y = 13 X = j)
P(X = j Y = 13) =
=
5
5
P(Y = 13 X = i)
=0
P(X = i)
P(Y = 13 X = i)
=0
since P(X = j) = 1/6 for j = 0, . . . , 5.
12
X
X
P(Y = 13 X = j) = 1
100
100
j
P(Y = 13 X = j) P(X = j Y = 13)
0
0.00000
0.0000
1
0.00886
0.0707
2
0.01569
0.1251
3
0.02082
0.1660
4
0.02451
0.1954
5
0.02702
0.2154
6
0.02856
0.2277
Total
0.12546
1
34
HELM (2008):
Workbook 37: Discrete Probability Distributions
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