Question: The random vector (X,Y,Z) follows a multivariate Normal distribution with mean vector 0 = (0,0,0) and covariance matrix 1 1 (249) In particular, X

The random vector (X,Y,Z) follows a multivariate Normal distribution with mean vector

The random vector (X,Y,Z) follows a multivariate Normal distribution with mean vector 0 = (0,0,0) and covariance matrix 1 1 (249) In particular, X and Z are independent. 1 (a) Define U Y - Z and W =Y+Z. What are respectively the marginal distri- butions of U and W? (b) Compute Cov(U, W). Are U and W independent? Explain your answer. (c) Obtain the conditional distribution of X, given W = Y + Z.

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