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 0.43 0.46 0.26 0 0.43 0.26 0.46 0 0 0 0 0.2 Q = 5 3 3 0 3 5 0 0 3 0 5 0 0 0 0 5 . Note that Q is simply the inverse of , 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? (c) [5 points] Please find the Markov blanket of X2. Recall that the Markov blanket of Xi is the set of variables (denoted by XMi ), such that Xi X{i}Mi | XMi , where {i} Mi denotes all the variables outside of {i} Mi. (d) [5 points] Assume that Y = [Y1, Y2] is defined by Y1 = X1 X4 Y2 = X2 X4. Please calculate the covariance matrix of Y