Find the bayes estimate and proportion The time between fail

Find the bayes estimate and proportion

The time between failures of a machine has an exponential distribution with parameter lambda . Suppose that the prior distribution for lambda is exponential with mean 100 hours. Two machines are observed, and the average time between failures is x = 1225 hours. (a) Find the Bayes estimate for lambda . (b) What proportion of the machines do you think will fall before 1000 hours? (a) lambda = _______________________ (Round your answer to five decimal places.] (b) The proportion of the machines is [Round your answer to three decimal places.]

Solution

x bar =1225 hours

Hence lemda = Bayes estimator = 1225

b) Machines that fail before 1000 hours = 0.33