Let X and Y be jointly distributed random variables. This exercise leads you through a proof of
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a. Express the quantity V(X − (σX/σY) Y) in terms of σX, σY, and Cov(X, Y ).
b. Use the fact that V(X − (σX/σY)Y) ≥ 0 and Cov(X, Y) = ρX,YσXσY to show that ρX,Y ≤ 1.
c. Repeat parts (a) and (b) using V(X + (σX/σY)Y) to show that ρX,Y ≥ −1.
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