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Let X1,,Xn be i.i.d. random variables with Poisson distribution P(Xi=k)=k!ek,k=0,1,2, Suppose the intensity parameter has a Gamma (,) distribution. (a) Find the posterior distribution of

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Let X1,,Xn be i.i.d. random variables with Poisson distribution P(Xi=k)=k!ek,k=0,1,2, Suppose the intensity parameter has a Gamma (,) distribution. (a) Find the posterior distribution of . (b) Calculate the posterior mean and variance. (c) Conclude whether or not the Gamma distributions form a conjugate family of Poisson distributions

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