Let X and Y be independent normal random variables Suppose that E(X) 1, E(Y ) 2, V (X) 3, V (Y ) 4 (1) Compute E(X 2 ) (2) Compute P (X Y ) (3) Let U X Y, W 2X Y Find E(U), E(W), V(U), V(W), and Cov(U,W) (4) Compute the conditional distribution of U given that W 4

Question: Let X and Y be independent normal random variables. Suppose that E(X) = 1, E(Y ) = 2, V (X) = 3, V (Y )

Let X and Y be independent normal random variables. Suppose that E(X) = 1, E(Y ) = 2, V (X) = 3, V (Y ) = 4.

(1) Compute E(X²).
(2) Compute P (X ≥ Y ).
(3) Let U = X +Y, W = 2X −Y. Find E(U), E(W), V(U), V(W), and Cov(U,W).
(4) Compute the conditional distribution of U given that W = 4.

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