2. (20 points) A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let $\mathrm{X}$ be the number of cash registers being used at a particular time for location 1 and $y$ the number being used at the same time at location 2 . The joint probability function is given by \begin{tabular}{ccccc} & & \multicolumn{3}{\c}{$y$} \ \cline { 3 - 5 }$f(x, y) $ & 0 & 1 & 2 \hline & O & $0.12$ & $0.04$ & $0.04$ W $x$ & 1 & 0& $0.24$ & $0.06$ & 2 & $0.08$ & $0.12$ & $0.30$ \end{tabular (a) Find $E(X)$ and $E(Y)$. (b) Find $\operatorname{Var} (x)$ and $\operatorname{Var}(Y)$. (c) Determine $E(XY)$ and correlation $ ho_{x, y]$. CS.VS. 1299