b) From part (a) now suppose that we observe a sample of size ten with z; = 21. Let the prior be specified with parameters a = 1 and 3 = 4. Find an estimate for the parameter A using the squared error loss L(@, a) = (e- a). Give your answer to two decimal places. Hint: If X- Gamma(a, 3) then E(X) = a,3. Question Three Let X,...,X, be ii.d. Poisson(A) and let A have a Gamma(a, 3) distribution with density of the form, f(z,a, 3) - T(a)3" the conjugate family for the Poisson. Find the posterior distribution for A.

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