Assume we have a multivariate normal random variable X= [X1, X2, X3, X4], whose covari- ance matrix and inverse covariance matrix Q are 0.71 -0.43 0.43 -0.43 0.46 -0.26 0 0.43 -0.26 0.46 0 0 0 0.2 0 II 5330 Y = X + X Y=X-X- X, LX-(i)UM, XM where {i} UM, denotes all the variables outside of {i}UM,. (d) [5 points] Assume that Y= [Y, Y2] is defined by Please calculate the covariance matrix of Y. 3500 3 Note that Q is simply the inverse of T, i.e., Q = 1. (a) [5 points] Are X3 and X4 correlated? (b) [5 points] Are X3 and X4 conditionally correlated given the other variables? That is, does cov(X3, X4 | X1, X2) equal to zero? 4050 (c) [5 points] Please find the Markov blanket of X2. Recall that the Markov blanket of X is the set of variables (denoted by XM,), such that 9000