Question: Suppose that X and Y are two random variables, which may be dependent, and Var(X) = Var(Y). Assuming that 0 < Var(X + Y) <

Suppose that X and Y are two random variables, which may be dependent, and Var(X) = Var(Y). Assuming that 0 < Var(X + Y) < ∞ and 0 < Var(X − Y)< ∞, show that the random variables X + Y and X − Y are uncorrelated.

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