Assume Y,..., Y02 id Normal(0, ) and ~ InvGamma(a, b). (a) Give an expression for two estimators of o: the posterior mean and the posterior mode. (b) Plot the posterior density functions and the give the two es timators for a sample with n = 10 and = 200 and a = b = 0.001. (c) Argue that both estimators are consistent (i.e., their MSE goes to zero as n increases) for any a and b.