Question: The time between failures of a machine has an exponential distribution with parameter . Suppose that the prior distribution for is exponential with mean

The time between failures of a machine has an exponential distribution with parameter λ. Suppose that the prior distribution for λ is exponential with mean 100 hours. Two machines are observed, and the average time between failures is x̅ = 1125 hours.

(a) Find the Bayes estimate for λ.

(b) What proportion of the machines do you think will fail before 1000 hours?

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