a) Let X1, . .., Xn be i.i.d. Poisson(A) and let ) have a Gamma(a, B) distribution with density of the form, f (x, a, P) = [( )Bar"-e-x/ B, 1 the conjugate family for the Poisson. Find the posterior distribution for 1. Gamma ( a+ )Xi+1, - B 1= 1 'nB + 1 O Gammaa + EXi, B i= 1 nB + 1 O Gamma ( o+ X; - 1, - B i= 1 n8 + 1 O Gamma at Xi,; 1 i=1 n3 +1 O Gamma ( o+ ) X; - 1, - 1 1= 1 nB + 1