5.26 Suppose that a data distribution for a random variable X follows the law N(0, 2), and that X,..., X, denotes a random sample from this distribution. Suppose further that for a prior distribution family you assume that (802) follows the natural conjugate distribution N(0, Ko) for some hyperpara- meters (B, K), where K denotes some pre assigned constant.

(a) Adopt an appropriate natural conjugate prior distribution family for a and evaluate the induced posterior distribution for (0, 02 | x1,...,x).

(b) Find the marginal posterior distribution for (8|x. .,xn).

(c) Find the marginal posterior distribution for ( | x.... X).