Page 294 - Applied Statistics And Probability For Engineers

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for is normal with 0 4 and 0 1. A random sample of (b) Compare the Bayes estimate with the maximum likeli-
n 25 observations is taken, and the sample mean is x 4.85. hood estimate.
(a) Find the Bayes estimate of . S7-6. The time between failures of a machine has an expo-
(b) Compare the Bayes estimate with the maximum likeli- nential distribution with parameter
. Suppose that the prior
hood estimate. distribution for
is exponential with mean 100 hours. Two
S7-5. The weight of boxes of candy is a normal random machines are observed, and the average time between failures
variable with mean and variance 1 10 pound. The prior dis- is x 1125 hours.
tribution for is normal with mean 5.03 pound. and variance (a) Find the Bayes estimate for
.
1 25 pound. A random sample of 10 boxes gives a sample (b) What proportion of the machines do you think will fail be-
mean of x 5.05 pound. fore 1000 hours?
(a) Find the Bayes estimate of .