Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f(t) = et, t> 0. From

Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f(t) = θe−θt, t> 0.

From prior experience we are led to believe that θ is a value of an exponential random variable with probability density

π(θ)=2e

−2θ

, θ> 0.

If we have a sample of n observations on T, show that the posterior distribution of Θ is a gamma distribution