Page 399 - Fundamentals of Probability and Statistics for Engineers

382 Fundamentals of Probability and Statistics for Engineers

4.20 3/4
4.231.53
1/2
1/2 1
2
2
2
4.25 [ 2 ‡ ) 2 ‡ ) ]
X 2 X 1 X 2 X 2 X 3
, 2 ‡ 2
4.27 a) m X 1 ‡ m X 2
X 1 1/2 X 2
2
/ 2 ‡ ) ; it approaches one if 2 2
b) X 2
X 1 X 2 X 2 X 1
4.28 n,2n
5jt
4.30 a) f t) ˆ e ,5,0
X
1
P 1 jtk
c) f t) ˆ k e ,2,2
X
kˆ1 2
2e jt 1 2 2 1
e) f t) ˆ 1 ‡ , ,
X
jt jt jt) 2 3 18
CHAPTER 5
5.1 (a)
0; for y < 8
8
>
>
1
<
F Y y†ˆ ; for 8 y 17
3
>
>
:
1; for y > 17
(b) 8
0; for y < 8
>
>
y 8
<
F Y y†ˆ ; for 8 y 17
9
>
>
1; for y > 17
:
5.3 8
0; for y < 1
>
>
y ‡ 1
>
>
>
> ; for 1 y < 2
9
<
f y†ˆ
Y
> 5 y
> ; for 2 y < 5
>
9
>
>
>
0; for y 5
:
5.5 8
1 ln y=2
2
< e ; for y 0
f y†ˆ y 2 † 1=2
Y
:
0; elsewhere
5.9 8
2
< ; for 0 x a
2 1=2
2
f x†ˆ a x †
X
:
0; elsewhere
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