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 ...

a Substituting This implies 1 0 or 1 b The same ...

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

Question:

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.