4. Let three random variables X1, X2, and X3 have a multivariate normal distribution with mean...

   

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4. Let three random variables X1, X2, and X3 have a multivariate normal distribution with mean vector =(1,2,3) and variance-covariance matrix: [3 2 1] = 2 2 1 1 1 1 a. Let Y = X-X2 + 2X3. Find E(Y) and Var(Y). b. Find P(X > X+X3-4). 5. Suppose Y=1(x > 0) and X~N(n, 1) where 1(A) = 1 if A is true; = P(Y - 1) (n) where () denotes the standard normal cdf. 0 if A is false. Show that 4. Let three random variables X1, X2, and X3 have a multivariate normal distribution with mean vector =(1,2,3) and variance-covariance matrix: [3 2 1] = 2 2 1 1 1 1 a. Let Y = X-X2 + 2X3. Find E(Y) and Var(Y). b. Find P(X > X+X3-4). 5. Suppose Y=1(x > 0) and X~N(n, 1) where 1(A) = 1 if A is true; = P(Y - 1) (n) where () denotes the standard normal cdf. 0 if A is false. Show that