Page 403 - Fundamentals of Probability and Statistics for Engineers

386 Fundamentals of Probability and Statistics for Engineers
^
9.7 1 is better
9.11 It is biased, but unbiased as n !1
2
2
9.14 a) /n, b) /n, c) 1 )/n, d) /n
2
4
9.15 /n,2 /n
1
9.20 a) 1 ,
X
9 k 1
X 1 1
b) 1 1
X X
kˆ1
^
^
9.22 A ML ˆ X 1) , A ME ˆ X 1
^
9.24 ˆ 0:13sec 1
^
^
9.26 a) ML ˆ ME ˆ T t 0 ) 1
^ ^
b) T 0 ML ˆ T 1) , T 0 ME ˆ T 1/ )
c)
^ 1 ^
ML ˆ‰T T 1† Š ; T 0 ML ˆ T 1†
^
2 1=2
2 1=2
^
ME ˆ M 2 T † ; T 0 ME ˆ T M 2 T †
1/2
9.30 2 )
9.32 a) l 1, 2 ˆ 63:65, 81:55, b) l 1, 2 ˆ 70:57, 84:43, c) l 1, 2 ˆ 77:74, 89:46
9.34 a) 9.16, b) l 1, 2 ˆ 8:46, 9:86
9.36 a) l 1, 2 ˆ 1072, 1128, b) l 1, 2 ˆ 1340, 6218 and l 1 ˆ 1478
9.38 384
CHAPTER 10
10.1 More likely to be accepted at ˆ 0:01
10.3 Hypothesis is accepted
10.5 Hypothesis is accepted
10.8 Poisson hypothesis is rejected
10.10 Gamma hypothesis is accepted
10.12 Normal hypothesis is accepted
10.14 Poisson hypothesis is accepted
10.16 Hypothesis is accepted

CHAPTER 11
11.1 (a)
! ! 1
n X
n
^
X
B ˆ x 2
x i Y i
i
iˆ1 iˆ1

TLFeBOOK