Page 400 - Fundamentals of Probability and Statistics for Engineers

Appendix C: Answers to Selected Problems 383

5.10 a)
8 1=2 ! 7:96 2 1=2 ! 6:96 3
0:19
> w=a† w=a†
>
< exp 5 ; for w > 0
4
f w†ˆ 2a w=a† 1=2 36:6 36:6
W
>
>
:
0; elsewhere
3
2
m W ˆ 1:71a 10 , 2 ˆ 8:05a 10 5
W
b) Same as a)
5.12 Y is discrete and
8
Z 1
f x†dx; for y ˆ 1
>
>
> X
0
<
p y†ˆ
Y Z 0
>
f x†dx; for y ˆ 0
>
>
: X
1
5.14 a)
1 2 2
8
< ; for 4 0:99r 0 † a 4 1:01r 0 †
f A a†ˆ 0:08r 0 a† 1=2
:
0; elsewhere
b)
8
2=3

1 3v 4 4

> 3 3
< ; for 0:99r 0 † v 1:01r 0 †
f v†ˆ 0:08 r 0 4 3 3
V
>
0; elsewhere
:
5.16 a)
2 ‡ y
8
; for 2 < y 0
>
>
4
>
>
<
f y†ˆ 2 y
Y
> ; for 0 < y 2
4
>
>
>
:
0; elsewhere
b) Same as a)
5.21
a 1 ‡a 2 ‡ ‡a n †t
a 1 ‡ a 2 ‡ ‡ a n †e ; for t > 0
f t†ˆ
T
0; elsewhere
Z 1
5.23 f y) ˆ f X 2 x 2 )[f X 1 x 2 ‡ y) ‡ f X 1 x 2 y)]dx 2 , 1 < y < 1
Y
1
5.25
2
ye y =2 ; for y 0
f y†ˆ
Y
0; elsewhere
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