(50 points) Random variables Wi, i = 1,2,3,4 are mutually independent stan- dard normal random variables. Random variables Xi, i = 1, 2, 3, 4 are gen- erated as follows. X1 = W1, X2 = W2 + 0.9X1, X3 = W3 +0.9X2 + 0.7X1, X4 = W4+ (1/2)W3+(1/4)W2+(1/8)W1. We would like to estimate X4 based on Xi, i = 1, 2, 3, so as to minimize the mean squared error (mse), using a linear estimator of the form Ẋ4 = a3 X3 + a2X2 + a X1. Find the values of aj, i = 1, 2, 3, and the resulting minimum mse E[(X4 - Ẋ 4)^2).