The time between failures of a laser in a cytogenics machine is exponentially distributed with a mean of 25,000 hours. (a) What is the expected time until the second failure? (b) What is the probability that the time until the third failure exceeds 50,000 hours? | Numerade
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The time between failures of a machine has an exponential distribution with parameter λ. Suppose that the prior distribution for λis 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? ? | Numerade
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