81. a.
.95
83. a.
.10, .20
b. 85. a.
b. c.
d. e.
for
87. a.
.40
b.
.571
c.
No: , and also
d.
.733
89. 91. a.
.333, .444
b.
.150
c.
.291
93.
.45, .32
95. a.
.0083
b.
.2
c.
.2
d.
.1074 [2p1 2 p]1 2 p
2
.40 2 .65.7 .571 2 .65
p 5 .5
.11 2 p
3
[.9 1 .11 2 p
3
] 5 .0137 .9 1 1 2 p
3
.1 1 2 p
3
1 2 1 2 p
n
p 2 2 p
97.
.905
99. a.
.956
b.
.994
101.
.926
103. a.
.018
b.
.601
105. a. .883, .117 b. 23
c.
.156
107. 109. a.
.0417
b.
.375
111.
for for for for
, so
is best.
113.
2 P
A
1
P A
2
P A
3
5 18 14 5 PA
1
¨ A
2
¨ A
3
s 5 1
s 5 3
s 5 2, and 5 624
s 5 1, 5 1024
s 5 0, 5 1124
P hire 1 5 624
1 2 1 2 p
1
1 2 p
2
c 1 2 p
n
Chapter 3
1.
for FFF; for SFF, FSF, and FFS;
for SSF, SFS,
and FSS; and for SSS
3.
of the two numbers, with possible values 22, 32, . . . , 122;
of the difference, with possible values 0, 1, 2, 3, 4, 5
5.
No. In Example 3.4, let if at most three batteries are
examined and let otherwise. Then Y has only two
values.
7. a.
{0, 1, . . . , 12} ; discrete
c.
{1, 2, 3, . . .}; discrete
e.
{0, c, 2c, . . . , 10,000c}, where c is the royalty per book; discrete
g.
where m M is the mini- mum maximum possible tension; continuous
9. a.
{2, 4, 6, 8, . . .} , that is, {21, 22, 23, 24, . . .}, an infinite sequence; discrete
b.
{2, 3, 4, 5, 6, . . .} , that is, {1 1 1, 1 1 2, 1 1 3, 1 1 4, . . .}, an infinite sequence; discrete
11. a.
, , , for ,
6, or 8
c.
.55, .15
13. a.
.70
b.
.45
c.
.55
d.
.71
e.
.65
f.
.45
15. a.
1, 2, 1, 3, 1, 4, 1, 5, 2, 3, 2, 4, 2, 5, 3, 4, 3, 5, 4, 5
b.
,
c.
for for for
, and for
17. a.
.81
b.
.162
c.
It is A; AUUUA, UAUUA, UUAUA, UUUAA;
.00405
19. 21. b.
.301, .176, .125, .097, .079, .067, .058, .051, .046 for
c.
for for for
for for
d.
.602, .301 x
9 8 x , 9, 5 1
2 x , 3, c
, 5 .954 1 x , 2, 5 .477
x , 1, 5 .301
F x 5 0
x 5 1, 2,
c , 9
p x 5
p 0 5 .09, p1 5 .40, p2 5 .32, p3 5 .19
2 x 5
1 1 x , 2
0 x , 1, 5 .9 x ,
0, 5 .3 F
x 5 0 p
1 5 .6, p2 5 .1 p
0 5 .3 x 2
4 p
x 5 0 p
8 5 .15 p
6 5 .40 p
4 5 .45 5x: m x M6
Y 5 Y 5
1 W 5
absolute value Z 5
average x 5
3 x 5
2 x 5
1 x 5
23. a.
.20
b.
.33
c.
.78
d.
.53
25. a.
for
27. a.
1234, 1243, 1324, . . . , 4321
b.
p 0 5 924, p1 5 824, p2 5 624, p3 5 0,
p 4 5 124
29. a.
6.45
b.
15.6475
c.
3.96
d.
15.6475
31.
.74, .8602, .85
33. a.
p
b. c.
p
35.
, , so 4 copies is better.
37.
,
39.
2.3, .81, 88.5, 20.25
43. 47. a.
.515
b.
.218
c.
.011
d.
.480
e.
.965
f.
.000
g.
.595
49. a.
.354
b.
.115
c.
.918
51. a.
6.25
b.
2.17
c.
.030
53. a.
.403
b.
.787
c.
.774
55.
.1478
57.
.407, independence
59. a.
.017
b.
.811, .425
c.
.006, .902, .586
61.
When , the probability is .99 for A and .9963 for B. If
, these probabilities are .75 and .6875, respectively.
63.
The tabulation for is unnecessary.
65. a.
20, 16
b.
70, 21
67.
when and when , compared to the upper bound of .25. Using
in place of , these probabilities are .002 and .004,
respectively, whereas the upper bound is .11. k 5
2 k 5
3 p 5
.75 5
.065 p 5
.5 P
|X 2 m| 2s 5 .042 p .
.5 p 5
.5 p 5
.9 E
X 2 c 5 EX 2 c, EX 2 m 5 0 n
2
2 112
E X
2
5 n 1 12n 1 16, VX 5 E
X 5 n 1 12 E
[h
4
X] 5 5.33 E
[h
3
X] 5 4.93 p
1 2 p y 5
0, 1, 2, 3, c
p y 5 1 2 p
y
p
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69. a.
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