5. Suppose that the joint distribution of $Y_1$, the number of contracts awarded to firm A, and
$Y_2$, the number of contracts awarded to firm B, is given by the entries in the following table.
\begin{tabular}{c|ccc}
$Y_1$ & \\
\hline
$Y_2$ & 0 & 1 & 2 \\
\hline
0 & 1/9 & 2/9 & 1/9 \\
1 & 2/9 & 2/9 & 0 \\
2 & 1/9 & 0 & 0 \\
\end{tabular}
a. Are $Y_1$ and $Y_2$ independent? Why?
b. Find $Cov(Y_1, Y_2)$. Does it surprise you that $Cov(Y_1, Y_2)$ is negative? Why?