Posted by haifeng on 2020-06-02 09:15:26 last update 2020-06-02 09:15:26 | Answers (1)
(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?
