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Let X1, ..., Xn be a random sample following Gamma(2, β) for some unknown parameter β >0.
(a) Now let's think like a Bayesian. Consider a prior distribution of β∼Gamma (a, b) for some a, b >0. Derive the posterior distribution of β given (X1, ..., Xn) = (x1, ..., xn).
(b) What is the posterior Bayes estimator of β assuming squared error loss?
(c) What is the distribution of ∑n i=1 Xi? You don't have to prove it.
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