A fair die is tossed twice. Let $X$ = the ssm of the faces, $Y$= the maximum of the two faces, and $Z$=|face 1 - face 2|.
write down the value of $X,Y,$ and $W=XZ$ for each outcome $w\in\ S$
I already found the value and range of $X,Y$ but I'm not sure how to find $W=XZ$. I saw someone post a similar question already answered however, it wasn't explained how to find $W=XZ$.
Since you said you've enumerated the outcomes for $X$, do the same for $Z$. Below I made a table for the values of both $X$ and $Z$. Can you now make the corresponding table for $W = XZ$? $$ \begin{array}{|c|c|c|c|c|c|c|} \hline X& 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ 6 & 7 & 8 & 9 & 10 & 11 & 12\\ \hline \end{array} $$
$$ \begin{array}{|c|c|c|c|c|c|c|} \hline Z & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 0 & 1 & 2 & 3 & 4 & 5 \\ 2 & 1 & 0 & 1 & 2 & 3 & 4 \\ 3 & 2 & 1 & 0 & 1 & 2 & 3 \\ 4 & 3 & 2 & 1 & 0 & 1 & 2 \\ 5 & 4 & 3 & 2 & 1 & 0 & 1 \\ 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ \hline \end{array} $$
For each outcome of the two rolls, find the values of $X$ and $Z$ and the value of $W$ is given by their product.
