Question: Let X u...,Xn be independent, identically distributed Poisson random variables with parameter 0 and let 11(0) be Gamma(a,p). (a) Show that the posterior density of

Let X u...,Xn be independent, identically distributed Poisson random variables with parameter 0 and let 11(0) be Gamma(a,p).

(a) Show that the posterior density of 0 given X x = x u ...,X n = is Gamma(a + 2?=1 xh (3 + n).

(b) Find the Bayes estimator of 0 with the squared-error loss.

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