Question 7 The Gamma distribution Gamma(a, ) is given by βαλα-le-βλ f(λ; α, β) = Γ(α) > where a and B are parameters of

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Question 7 The Gamma distribution Gamma(a, ) is given by βαλα-le-βλ f(λ; α, β) = Γ(α) > where a and B are parameters of the distribution, and r) is the Gamma function (see Lecture 1 if you don't remember what this function is), with derivative denoted by L'O). Show that it is a conjugate prior of Poisson(a), i.e., when the observations Xį for 1 <i<n are independent identically distributed random variables with PDF equal to > e-xi fx: (xi) = em Xi! the posterior distribution also follows a Gamma distribution. What are its parameters?