Fundamentals of Probability and Statistics for Engineers

4.20

4.25

4.27

4.28

4.30

CHAPTER 5

5.1 (a)

(b)

5.3

5.5

5.9

382 Fundamentals of Probability and Statistics for Engineers

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4.2 31.5 3
^2 X 2 [^2 X 1 ‡^2 X 2 )1/2^2 X 2 ‡^2 X 3 )1/2]^1
a)mX 1 ‡mX 2 ,^2 X 1 ‡^2 X 2
b)X 2 /^2 X 1 ‡^2 X 2 )1/2; it approaches one if^2 X 2 ^2 X 1
n,2n
a)fXt)ˆe^5 jt,5,0

c)fXt)ˆ

P^1

kˆ 1

1

2 k

ejtk,2,2

e)fXt)ˆ

2ejt

jt

1 

1

jt



‡

2

jt)^2

,

2

3

,

1

18

FY…y†ˆ

0 ; fory< 8

1

3

; for 8y 17

1 ; fory> 17

8

>>

<

>>

:

FY…y†ˆ

0 ; fory< 8

y 8

9

; for 8y 17

1 ; fory> 17

8

>>

<

>>

:

fY…y†ˆ

0 ; fory< 1

y‡ 1

9

; for 1 y< 2

5 y

9

; for 2y< 5

0 ; fory 5

8

>>

>>

>>

<

>>>

>>

>:

fY…y†ˆ

1

y… 2 †^1 =^2

eln

(^2) y= 2
; fory 0
0 ; elsewhere

8

<

:

fX…x†ˆ

2

…a^2 x^2 †^1 =^2

; for 0xa

0 ; elsewhere

8

<

: