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In: Statistics and Probability

For a random sample of sizenfrom an Exponential distribution with rate parameter λ (so that the...

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.)

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