Let three random variables X1 X2 and X3 have a multivariate

Let three random variables X_1, X_2, and X_3 have a multivariate normal distribution with mean vector mu = (1, 2, 3) and variance-covariance matrix: Sigma = [3 2 1 2 2 1 1 1 1] Let Y = X_1 - X_2 + 2X_3. Find E(Y) and Var(Y). Find P(X_1 > X_2 + X_3- 4). Suppose Y = 1(X > 0) and X~N(eta, 1) where 1(A) = 1 if A is true; = 0 if A is false. Show that P(Y = 1) = Phi(eta) where Phi( ) denotes the standard normal cdf.

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