Fundamentals of Probability and Statistics for Engineers

3.17

3.19

3.22

3.26

ij

1234567

1 0.006 0.004 0.003 0.003 0.004 0.000 0.000

2 0.002 0.009 0.008 0.005 0.010 0.002 0.001

3 0.003 0.008 0.015 0.014 0.031 0.008 0.005

4 0.001 0.004 0.015 0.027 0.051 0.017 0.011

5 0.002 0.007 0.029 0.054 0.196 0.075 0.050

6 0.001 0.002 0.005 0.015 0.071 0.060 0.032

7 0.000 0.001 0.005 0.008 0.052 0.030 0.038

CHAPTER 4

4.1

4.6

4.12

4.14

4.16

4.19

Appendix C: Answers to Selected Problems 381

pX…x†ˆ

0 : 6 ; forxˆ 1

0 : 4 ; forxˆ 2



pY…y†ˆ

0 : 6 ; foryˆ 1

0 : 4 ; foryˆ 2



3 :1 3a): i)

iii)f

X…x†ˆ

ex; forx 0

0 ; elsewhere



fY…y†ˆ

ey; fory 0

0 ; elsewhere



b): i) No, iii) Yes

[FXx)FX100)]/[1FX100)],x 100

a) 0.087, b) 0.3174, c) 0.274

0.0039

a)

pX 3 …x†ˆ

0 : 016 ; forxˆ 1

0 : 035 ; forxˆ 2

0 : 080 ; forxˆ 3

0 : 125 ; forxˆ 4

0 : 415 ; forxˆ 5

0 : 192 ; forxˆ 6

0 : 137 ; forxˆ 7

8

>>>

>>

>>

<

>>

>>>

>

b) Table ofpX 4 X 3 i,j)

a) 5, 0; c) 2, 2; e)a/a‡1),a/[a‡1)^2 a‡2)]; g) 1, 3

4. 32.44 min
   a) 1/2, b) 2, 4; c) 0, 1
   a) 1p)/, b) 1/
   24 min
   PjX 1 j 0 :75) 0 :41 by the Chebyshev inequality,PjX 1 j 0 :75)
   ˆ 0 : 75
   a)P55X85) 0
   b)P55X85)5/9, much more improved bound

: