[Exer15-4] Exercise 35 of Book {Devore2017B} P.221
- (a) Use the rules of expected value to show that $\mathrm{Cov}(aX+b,cY+d)=ac\mathrm{Cov}(X,Y)$.
- (b) Use part (a) along with the rules of variance and standard deviation to show that $\mathrm{Corr}(aX+b,cY+d)=\mathrm{Corr}(X,Y)$ when $a$ and $c$ have the same sign.
- (c) What happens if $a$ and $c$ have opposite signs?