Show that mixtures of natural conjugate priors, as defined in (4.1), form a conjugate class of priors.
Find the posterior mean and posterior variance or covariance matrix in Exercise (a) 5, (b) 6, (c) 7, (d) 8, (e) 9, (f) 10, (g) 11, (h) 12(b), (i) 12(c), U) 14, (k) 15, (I) 16(b), (m) 16(c), and (n) in Example 5.
Find the generalized maximum likelihood estimate of 8 and the posterior variance or covariance matrix of the estimate in Exercise (a) 5, (b) 6, (c) 7, (d) 8, (e) 9, (f) 10, (g) 11, (h) 12(c), (i) 14, U) 15, (k) 16(c), and (1) in Example 5.