How to calculate XY? If I have two independent random variables, how should I calculate the product of them?
For example:

How should I calculate XY? 
Thank you.

You can just make a table
$$\begin{bmatrix}
X \text{\\} Y && 1 && 4 && 6 \\
2 && .12 && .04 && .04 \\
3 && .18 && .06 && .06 \\
5 && .30 && .10 && .10
\end{bmatrix}$$
So $P(XY= x\cdot y)=P(X=x)P(Y=y)$ and you get the table from there. In general if you have any overlap of products, you would need to add them together, in this case there are no duplicates, so you just have that table, but if eg $X$ had a $4$ value and $Y$ had a $2$ value, then $X=4, Y=1$ and $X=Y=2$ would both contribute to $P(XY=4)$.
