Let X and Z be jointly Gaussian vectors with means and covariance given by

2. Let X and Z be Gaussian vectors with means and covariance given by 5 5 9 EX] EZ] (=1) , Cov( X] , 2" ]] ) = 5 = 1 1 3 4 Let Y be obtained from X and Z as 2 0 (2 2 Y = 0.5 x 3 3 X +0.5 x 1 1/2 Z. a) Find E[Y X], the best estimator of Y given X. b) Compute the LMMSE E[Y|X] and E[XY]