a. Use the general formula for the variance of a linear combination to write an expressi...

a. Use the general formula for the variance of a linear combination to write an expression for V( a X +Y). Then let and show that ρ ≥ – 1. [Hint: Variance is always ≥ 0, and Cov(X, Y ) = σ_X _ σ_Y _ ρ.]

b. By considering V(aX _ Y ), conclude that r _ 1.

c. Use the fact that V(W) = 0 only if W is a constant to show that ρ = 1 only if Y = aX + b.