Let X and Y be random variables such that 0 < 2X < and 0 <

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.