Page 401 - Fundamentals of Probability and Statistics for Engineers

384 Fundamentals of Probability and Statistics for Engineers

5.27
8 2
3y
>
< ; for y 0
f y†ˆ 1 ‡ y† 4
Y
>
0; elsewhere
:
5.29
2
r r =2 2
e ; for r 0; and
f R r; †ˆ 2 2
0; elsewhere
2
r r =2 2
e ; for r 0
f r†ˆ 2
R
0; elsewhere
8
1
< ; for
f †ˆ 2

0; elsewhere
:
R and are independent
CHAPTER 6

6.3 a) 0.237, b) 3.75
6.5 0.611, 4.2
m
n
X n k
k
6.8 a) 1 p 1 p)
k
kˆ0
n

X n n k
k
b) k m) p 1 p)
k
kˆm‡1
6.10 0.584
s‡r 1
X k 1 r k r
6.12 p 1 p)
r 1
kˆr
6.14 0.096
6.17 a) 0.349, b) 5
6.26 0.93
6.28 1:4 10 24
k 22:5
6.30 p k) ˆ 22:5 e /k!, k ˆ 0, 1, 2, ...
X
v
k v
t exp t /w)
6.32 p 0, t) ˆ , k ˆ 0, 1, 2, ...
k
w k!

TLFeBOOK