4.2-9. Let the joint pmf of X and Y be
$f(x, y) = 1/4$,
$(x, y) \in S = \{(0,0), (1, 1), (1, -1), (2,0)\}$.
(a) Are X and Y independent?
(b) Calculate $Cov(X, Y)$ and $\rho$.
This exercise also illustrates the fact that dependent random variables can have a correlation coefficient of zero.