Problem 4. Let X1, ..., Xn ~N(B, 62), and suppose that the prior distri- bution on 0 is N(u, 72). (Here we assume that o', u and 72 are all known. (1) Prove that the posterior distribution of 0 is also normal, with mean and variance given by 82 E(0| Xn) = T2 + 02 / n Xn + 82 / n+ T2RX, 02+2 Var(0|Xn) = 8 2 + NT 2 (2) How will the posterior distribution look like when n - co