Q$.2.($a$)$ If $x$ and $Y$ are two discrete random variables, show that $E(x+Y)=E(x)+E(Y)$

where $E(x)$ is the expected value of $x.$

Hence, find mean of $Z=2x-3Y,$ where $x$ and $Y$ are discrete random variables with means $3$ and $5$ respectively.

$\frac{61}{2}$