The time between failures of a machine has an exponential distribution with parameter

Chapter 7, Problem 7-50

(choose chapter or problem)

The time between failures of a machine has an exponential distribution with parameter . Suppose that the prior distribution for is exponential with mean 100 hours. Twomachines 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 before 1000 hours?

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