Page 402 - Fundamentals of Probability and Statistics for Engineers

Appendix C: Answers to Selected Problems 385

CHAPTER 7

7.1 0.847
7.3 (a) 0.9, (b) 0.775

3
7.6 (a) 4.566 10 , (b) 0.8944, (c) 0.383, (d) 0.385
7.9 X 2 is preferred in both cases
7.14 0.0062
7.20 (a) 0.221
(b)
8
1 1 y a
> 2
< exp ln ; for y a
f y†ˆ 0:294† 2 † 1=2 y a† 0:172 0:958b
Y
>
0; elsewhere
:
m Y ˆ a ‡ b
7.22 0.153
7.30 (a) 0.056, (b) 0.989
7.34 0.125, 0, 0, 0.875. No partial failure is possible
7.36
1
8 Z
n 2
n n 1† ‰F X y† F X y s†Š f y s†f y†dy; for s 0
<
X
X
f s†ˆ 1
S
0; elsewhere
:
CHAPTER 8
8.2 (a) (i) Type-1 asymptotic maximum-value distribution is suggested
(ii)  0.025, u  46.92
(d) (i) Gamma is suggested, (ii)  0:317
(f) (i) Poisson is suggested, (ii) v  45:81
(h) (i) Normal is suggested, (ii) m  2860,  202:9
(j) (i) Poisson is suggested, (ii) v  7:0
(i) (i) Lognormal is suggested, (ii) X  76:2, 2 ln X  0:203

CHAPTER 9
9.1 1.75, 27.96
9.5 (a)
9
10y ; for 0 y 1
f y†ˆ
Y
0; elsewhere
9
10 1 z† ; for 0 z 1
f z†ˆ
Z
0; elsewhere
(c) 0.091, 0.91

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