31.

a. Use the rules of expected value to show that Cov(aX 

b, cY 

d)  ac Cov(X, Y).

b. Use part

(a) along with the rules of variance and standard deviation to show that Corr(aX  b, cY 

d)  Corr(X, Y ) when a and c have the same sign.

c. What happens if a and c have opposite signs?