Let X1, X2, , Xn be Poisson random variables with parameter Assume that has a Gamma (a, b) prior (a) Compute the posterior distribution of (b) Obtain the Bayes estimate of (c) Compare the MLE of with the Bayes estimate of (d) Which of the two estimates is better Why

Question: Let X1, X2, . . ., Xn be Poisson random variables with parameter . Assume that has a Gamma (a, b) prior. (a) Compute

Let X1, X2, . . ., Xn be Poisson random variables with parameter λ. Assume that λ has a Gamma (a, b) prior.
(a) Compute the posterior of λ.
(b) Obtain the Bayes estimate of λ.
(c) Compare the MLE of λ with the Bayes estimate of λ.
(d) Which of the two estimates is better? Why?

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