16.2* Suppose there are three bivariate normal populations with training sample statistics as in Exercise 16.1, but, in addition, we know N = N = N = N = 10, and x = (0, 0), S = ( }). 3 Assuming the prior odds for all three populations are the same, classify z = (2.2)' into one of the three populations. 16.3* For the classification problem in Section 16.1 adopt a natural conjugate prior family for (0,, A), instead of the vague prior family used there, and find:

(a) The joint posterior density of 0,, A, given (,, V,, ;);

(b) The predictive density of (z | x, V, ); "

(c) The posterior classification probability for classifying z into ,, given z. that is Plzen, z}.