a Use the general formula for the variance of a linear combination to write an expression for V(aX Y) Then let a Y X, and show that 1 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 1 only if Y aX b

Question: a. Use the general formula for the variance of a linear combination to write an expression for V(aX + Y). Then let a = Y/X,

a. Use the general formula for the variance of a linear combination to write an expression for V(aX + Y). Then let a = σY/σX, and show that ρ ≥ - 1.
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.

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