In: Statistics and Probability
For a random sample of sizenfrom an Exponential distribution with rate parameter λ (so that the density is fY(y) =λe−λy), derive the maximum likelihood estimator, the methods of moments estimator, and the Bayes estimator (that is, the posterior mean) using a prior proportional to λe−λ, for λ >0. (Hint: the posterior distribution will be a Gamma.)