Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f (t) = ? c ^{?? t}, t > 0. From prior experience we are led to believe that. 0 is a value of an exponential random variable with probability density ? (?) = 2^e-2?, 0 > 0. If we have a sample of n observations on T, show that the posterior distribution of ? is a gamma distribution with parameters.

Transcribed Image Text:

,3 = (E+ and a = n + 1.