Q1. Consider the random variables Y1, Y2, X1, X2 such as Cov(Y1, X1) = 2; Cov(Y1, X2) = 12; Cov(Y2, X1) = 3; Cov( Y2, X2) = 7. Suppose that E[X]] = E[X2] = 0, but E[Y]] = E[Y2] = 5, besides, Var(Y1) = Var(Y2) = 10 and Var(X1) = Var(X2) = 9. Cov(X2, X1) = 0; Cov( Y2, Y1) = 0. (a) Determine the best linear prediction of Y1 given that X1, X2 and give the corresponding mean square predicted error. (b) Determine the best linear prediction of Y2 given that X1, X2 and give the corresponding mean square predicted error. (c) Determine the best linear prediction of Y1 - Y2 given that X1, X2 and give the corresponding mean square predicted error