Let X and Y be random variables such that 0 2X and 0 2Y Suppose that U aX b and V cY d, where a 0 and c 0 Show that (U, V ) (X, Y) if ac 0, and (U, V ) (X, Y) if ac 0

Question: Let X and Y be random variables such that 0 < 2X < and 0 < 2Y < . Suppose that U = aX

Let X and Y be random variables such that 0 < σ2X < ∞ and 0 < σ2Y < ∞. Suppose that U = aX + b and V = cY + d, where a ≠ 0 and c ≠ 0. Show that ρ(U, V ) = ρ(X, Y) if ac > 0, and ρ(U, V )=−ρ(X, Y) if ac < 0.

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