Chapter 4.2, Problem 9E

Let the joint pmf of X and Y be $f\left(x,y\right)=\frac{1}{4}\text{, }\left(x,y\right)\in S=\left\{\left(0,0\right),\left(1,1\right),\left(1,-1\right),\left(2,0\right)\right\}$.

(a) Are X and Y independent’

(b) Calculate Cov(X, Y) and p.

This exercise also illustrates the fact that dependent random variables can have a correlation coefficient of zero.