9. (7 points) Three fair dice are rolled. Find the probability mass function of the product of the three numbers appearing given that their sum is 5. Hint: . Call the relevant pmf f(2) on the appropriate support. . First compute the number of equally likely possible rolls of three fair dice. . List all of the possible 3-tuples where the rolls add to 5. (order does not matter here). . Now list the number of permutations for each of the 3-tuples that you listed. . Now write down the product of the 3 rolls for each of your 3-tuples. . Let S be the event that the sum is 5, and compute Pr(S). . Let Mi be the event that the product is i. . Compute Pr(Sn Mi). . Finally compute Pr(Mi|S) for relevant