Suppose that X,Y are both standard normal random variables and Cov(X,Y) = 1 (a) Compute E (X² – Y²)| (b) Is it possible to compute P (X +Y > 3) from the given information? If so compute, otherwise explain.
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- If X is a random variable having the standard normaldistribution and Y = X2, show that cov(X, Y) = 0 eventhough X and Y are evidently not independent.Assume Z1, Z2, . . . , Zn are independent standard normal random variables. The random variable Y defined byIf X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?