Please assist in this homework practical. Please provide full working out for future practice.

Suppose that X1 ~ N(1, 2), X, ~ N(2, 4) and Cou(X, X2) = 1. Let 11 X = = Y = Y2 Ya and Y = AX. We also assume that X - N,(ex. Cx). In (a) and (b) find in a matrix form (a) (1 Marks) the mean of Y. (b) (2 Marks) the variance-covariance matrix of Y. Show your working. 2 (c) (2 Marks) What is the distribution of Y? (d) (2 Marks) Find the distribution of 3Y, - 212. Provide also the mean and the variance of 3Yi - 212- (e) (3 Marks) Identify the joint distribution of Z1 = 3Y1 - 212 and Za = -312 - Ya Provide also the mean and the variance of Z = Zz