Question

Gaussian Multivariate Assume we have a multivariate normal random variable X = [X1, X2, X3, X4]T whose covariance matrix Î£ and inverse covariance matrix Q are: Î£ = [0.71, 0.43, 0.43, -0.43; 0.43, 0.46, 0.26, 0.2; 0.43, 0.26, 0.46, -0.3; -0.43, 0.2, -0.3, 0.5] Note that Q is simply the inverse of Î£, i.e. Q = Î£^(-1). Are X3 and X4 correlated? Are X2 and X4 conditionally correlated given the other variables? That is, does cov(X3, X4 | X1, X2) equal to zero? (c) Please find the Markov blanket of X2. Recall that the Markov blanket of Xi is the set of variables (denoted by Xi;), such that Xi âŠ¥ {Xj} \ {Xi}, where âŠ¥ denotes independence. Assume that Y = [Y1, Y2]T is defined by: Y1 = X1 + X2 Y2 = X3 - X4 Please calculate the covariance matrix of Y.

          Gaussian Multivariate

Assume we have a multivariate normal random variable X = [X1, X2, X3, X4]T whose covariance matrix Î£ and inverse covariance matrix Q are:

Î£ = [0.71, 0.43, 0.43, -0.43; 0.43, 0.46, 0.26, 0.2; 0.43, 0.26, 0.46, -0.3; -0.43, 0.2, -0.3, 0.5]

Note that Q is simply the inverse of Î£, i.e. Q = Î£^(-1).

Are X3 and X4 correlated? Are X2 and X4 conditionally correlated given the other variables? That is, does cov(X3, X4 | X1, X2) equal to zero?

(c) Please find the Markov blanket of X2. Recall that the Markov blanket of Xi is the set of variables (denoted by Xi;), such that Xi âŠ¥ {Xj} \ {Xi}, where âŠ¥ denotes independence. Assume that Y = [Y1, Y2]T is defined by:

Y1 = X1 + X2
Y2 = X3 - X4

Please calculate the covariance matrix of Y.

gaussian multivariate assume we have a multivariate normal random variable x xixzx3 xat whose covari ance matrix 2 and inverse covariance matrix q are 071 043 043 043 046 026 5 043 026 046 0 51984

Added by Thomas M.

Question

Please give Ace some feedback