Question: We are interested in estimating the constant failure rate of a pump. A prior assessment of value of the failure rate, lambda, follows a Gamma

We are interested in estimating the constant failure rate of a pump. A prior assessment of value of the failure rate, lambda, follows a Gamma distribution with parameters a=2.5 and b =250. A test involving 10 pumps identical to the pump in question is conducted for 100 hrs during which one pump fails 50 hrs after start of the test. Find the posterior distribution of the failure rate lambda

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