3. Find the maximum likelihood estimates of the 2 x 1 mean vector u and the 2 x 2 covariance matrix E based on the random sample 3. 6' 4 X = 4 \4 7/ from a bivariate normal population. [5 + 12 marks] 4. Let X be N3 (u, E) with u' = (2 -3 1) and 1 1 1 1 2 1 Find: (a) The marginal distribution of 3X1 - 2X2 + X3. (10 marks) (b) The marginal distribution of [2 marks) (X3/ 2X1 X2 + 4X3 -2X2 + 3X3 [8 marks] (c) The joint distribution of (X2) (d) The conditional distribution of (X3) given X, = -3. [19 marks)