You choose randomly two distinct elements from the set $\{-2,-1,0,1,2\}$.
We denote by $X$ the random variable that is equal to the product of the two previously chosen elements.
I have to find the PMF of $X$, $E[X]$ and $Var(X)$ and I did find them but using the classical method by applying the usual formulas it was very easy but also too long.
Do you guys know a shortcut or some tricks to solve this kind of exercise?
The results I've found:
$E[X] = -0.5$ and $Var(X) = 3.05$