3. [20 points] X is a 3-dimensional random vector with E X - 0 and a correlation matrix Rx with elements Rx(i, j) - 1- 0.25 2 - j . Y is a 2-dimensional random vector with M = X1 + X2 Y2 - X2 + X3 We observe Y = [Y1 Y2 and use it to form a linear estimate of X1, as X1 - a1 Yi + a2Y2. (a) What are the optimum coefficients a1, a that result in the smallest MSE for estimating X1 ? (b) What is the resulting MSE of the estimator you found in part (a)? (c) We now only use Y, to form a linear estimate of X1 as X1 = a)1 + b. What are the optimum coefficients a and b ? What is the resulting MSE ? How does it compare to the MSE obtained in the previous part