Let X1, . . . , Xn be a random sample following Gamma(2, β) for some...

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Let X1, . . . , Xn be a random sample following Gamma(2, β) for some...

Let X1, . . . , Xn be a random sample following Gamma(2, β) for some unknown parameter β > 0.

(i) 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).

(j) What is the posterior Bayes estimator of β assuming squared error loss?

math Statistics-And-Probability

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