1.(6') Find the correlation $\rho_{x,y}$ between two random variables X and Y
if (X, Y) have the joint PMF
\begin{align*}
(a) \ p(x, y) = \frac{1}{3} \text{ for } (x, y) = (0,0), (1,1), (2,2) \text{ and zero elsewhere.}\\
(b) \ p(x, y) = \frac{1}{3} \text{ for } (x, y) = (0,2), (1,1), (2,0) \text{ and zero elsewhere.}
\end{align*}
