Applied Statistics and Probability for Engineers

7-6

for is normal with  0 4 and 1. A random sample of

n25 observations is taken, and the sample mean is

(a) Find the Bayes estimate of .

(b) Compare the Bayes estimate with the maximum likeli-

hood estimate.

S7-5. The weight of boxes of candy is a normal random

variable with mean and variance pound. The prior dis-

tribution for is normal with mean 5.03 pound. and variance

pound. A random sample of 10 boxes gives a sample

mean of pound.

(a) Find the Bayes estimate of .

x5.05

(^1)  25
(^1)  10
x4.85.
^20 (b) Compare the Bayes estimate with the maximum likeli-
hood estimate.
S7-6. The time between failures of a machine has an expo-
nential distribution with parameter. Suppose that the prior
distribution for is exponential with mean 100 hours. Two
machines are observed, and the average time between failures
is hours.
(a) Find the Bayes estimate for.
(b) What proportion of the machines do you think will fail be-
fore 1000 hours?
x 1125
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