QUESTION 5 (a) Let Y and Y have a bivariate normal distribution. Show that the conditional distribution of Y given that Y = 1/ is a normal distribution with mean +(2-) and variance (1-). (10) X (b) Consider the following bivariate joint probability density function for the random vector [[M] fxy(x, y) 1 21-pa,ay +(-)"}]. exp 1-0-7 2 (1-) {(1 2( S(x-1) (-)(x-H) 2p- where a > 0, 0, >0, and p < 1. Then fxy(x, y) is such that =[ = (x My) x2 == - pa,ay pagay 0 "]. Given that Jr.x. (01, 12) = exp[-(20 + 12 + 2/192 22y1 1492 + +65}], [24] is the density of a bivariate normal random vector Y = (Y Y ), find (1) E[Y]. (ii) Var[Y] and (iii) k. 1847/48 -8