Let X1, . . . , Xn ∼ iid Gamma(3,1/θ) and we assume the prior for θ is InvGamma(10,2).(a) Find the posterior distribution for θ.(b) If n = 10 and ¯x = 18.2, find the Bayes estimate under squared error loss.(c) The variance of the data distribution is ϕ = 3θ2. Find the Bayes estimator (under squared error loss) for ϕ.

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