Let X and Y be random variables with finite variance. Prove that |(X, Y)| = 1 implies

Let X and Y be random variables with finite variance. Prove that |ρ(X, Y)| = 1 implies that there exist constants a, b, and c such that aX + bY = c with probability 1. Use Theorem 4.6.2 with U = X − μX and V = Y − μY.