Random Variables - Rolling two fair six-sided dice Consider rolling two fair six-sided dice. Let W be the product of the number showing. What is the probability function of W?
I have a hard time figuring out how to solve this question. 
Any help will be appreciated! 
 A: Each distinct pair has probability 1/36 by fairness and independence of trials. For each pair compute the product and sum together all pairs that give the same product. For example the product 1 only occurs for the pair (1,1). So its probability is 1/36. For 36 only the pair (6,6) yields 36. So the probability of 36 is also 1/36. On the other hand the pairs (1,2) and (2,1) are the only pairs that yield the product 2. Now the product 4 occurs for (1,4), (4,1) and (2,2). So the product 4 has probability 3/36 or 1/12. Proceed in the same way to get the probabilities for the products 3, 5, 6, 8, 9, 10, 12, 15. 16, 18, 20, 24, 25, and 30 to get the full distribution.
Note that (1,3) and (3,1) yields 3, (1,5) and (5,1) yields 5, (3,2) and (2,3) and (6,1) and(1,6) yields 6, (4,2) and (2,4) yields 8, (3,3) yields 9, (5,2) and (2,5) yields 10, (4,3) and (3,4) and (6,2), (2,6) yields 12, (3,5) and (5,3) yields 15, (4,4) yields 16 (3,6) and (6,3) yields 18, (5,4) and (4,5) yields 20, (6,4) and (4,6) yields 24, (5,5) yields 25 and (5,6) and (6,5) yields 30.
