5.27
5.29
and are independent
CHAPTER 6
6.3
6.5
6.8
6.10
6.12
6.14
6.17
6.26
6.28
6.30
6.32
384 Fundamentals of Probability and Statistics for Engineers
fY
y
3 y^2
1 y^4
; fory 0
0 ; elsewhere
8
><
>:
fR
r;
r
2 ^2
er
(^2) = 2 2
; forr 0 ;and
0 ; elsewhere
fR
r
r
^2
er
(^2) = 2 2
; forr 0
0 ; elsewhere
f
1
2
; for
0 ; elsewhere
8
<
:
R
a) 0.237, b) 3.75
0.611, 4.2
a) 1
Xm
k 0
n
k
pk1p)nk
b)
Xn
km 1
km)
n
k
pk1p)nk
0.584
sXr 1
kr
k 1
r 1
pr1p)kr
0.096
a) 0.349, b) 5
0.93
1 : 4 10 ^24
pXk) 22 : 5 ke^22 :^5 /k!,k0, 1, 2,...
pk0,t)
tv
w
k
exp tv/w)
k!
,k0, 1, 2,...