1. Suppose the covariances between X, and X2 is 5, between X1 and X3 is 4, and between X2 and X3 is 0. Moreover, the variances of X1, X2, X3 are 49, 25,9, respectively. (a) Write the 3x3 covariance (2) and correlation (/) matrices of the random vector X = (X1, X2, X3). For the next parts use the fact that for any scalars a1, a2, a3: Var(an Xi + a2X2 + a3X3) = a; Var(X1) + a; Var(X2) + a;Var(X3) + 2ajazCov(X1, X2) + 2aja;Cov(X1, X3) + 2aza;Cov(X2, X3). (b) Use the above formula and compute the (numerical) value of Var(a, X, + 02X2 + a;X3) for the following choices of a = (a1, 02, 03): 1. a = (2, -2,0), 2. a = (2, -1,5), 3. a = (-1, 1,2), 4. a = (-81, -82,1). (c) Derive the normal equations for minimizing Q(b1, b2) = Var(X3-bjX1 - b2X2), assuming that the random variables have means equal to zero. Remember that normal equations are obtained by setting the partial derivatives to zero. (d) Write the equations in (c) in matrix form first, then solve it for b, and by. (e) (Bonus) Compute the inverse of the covariance matrix _ in (a)