CHAPTER 3
3.1 (a)
(c)
(e)
(g) neither pdf nor pmf exists
3.2 (a)
(b)
3.4 (a)
(b)
(c)
3.11
3.12
380 Fundamentals of Probability and Statistics for Engineers
a1,
p
x
1 ; forx 5
0 ; elsewhere
a2,px)
1
2 x
, forx1, 2,...
a>0,
f
x ax
a (^1) ; for 0x 1
0 ; elsewhere
ora0,
p
x
1 ; forx 0
0 ; elsewhere
a 1/2,
1, 1/3, 63/64, 1e^6 a,1,1,2e1/3)/2
1, 1, 127/128,ea/2e^7 a,11/2)a, 1/2, e1/4e7/2)/2
FX
x
0 ; forx< 90
0 : 1 x 9 ; for 90x< 100
1 ; forx 100
8
<
FX
x
0 ; forx< 0
2 xx^2 ; for 0x 1
1 ; forx> 1
8
<
FXx)
1
tan^1 x
1
2
, for1<x< 1
3.6 2/3
3.9
FX
x
0 ; forx< 0
x
b
; for 0xb
1 ; forx>b
8
><
>:
fX
x
1
b
; for 0xb
0 ; elsewhere
8
<
:
3/a
b) 1/6