I'm trying to obtain the PMF of the product of two dice. I've made the following table:
\begin{array} {|r|r|}\hline product & occurrence \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 2 \\ \hline 4 & 3 \\ \hline 5 & 2 \\ \hline 6 & 4 \\ \hline 8 & 2 \\ \hline 9 & 1 \\ \hline 10 & 2 \\ \hline 12 & 4 \\ \hline 15 & 2 \\ \hline 16 & 1 \\ \hline 18 & 2 \\ \hline 20 & 2 \\ \hline 24 & 2 \\ \hline 25 & 1 \\ \hline 30 & 2 \\ \hline 36 & 1 \\ \hline \end{array}
What could work as a possible PMF from this data? Can an expression for the product of two dice be given like the one for the sum: $p_k = \frac{6-|k-7|}{36}$ ?
Thank you.