Question: Suppose that X and Y have a bivariate normal distribution. (a) Prove that X +Y has a normal distribution when X and Y are standard

Suppose that X and Y have a bivariate normal Prove that X +Y has a normal when X and Y are standard normal random variables.
(b) Find E(cX + dY) and Var(cX + dY) in terms of μX,μY,σX,σY , and ρ(X, Y), where X and Y are arbitrary normal random variables.

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