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Let X1, . . . , Xn be i.i.d. random variables with Poisson distribution P(Xi = k|) = e k k! , k = 0,

Let X1, . . . , Xn be i.i.d. random variables with Poisson distribution P(Xi = k|) = e k k! , 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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