D 2. (18 points) Consider tossing two six-sided dice. As is often the case, you may want to write out the sample space of the experiment before you begin. Let X be the sum of the two dice and Y be the absolute value of difference of the two dice, so that Y({5,3}) = Y({3,5}) = 2. Create a table showing the joint pmf of X and Y, f(x, y). You do not have to submit this table, but it will be helpful for answering the following questions. C 2.1. What is f(8,0)? 2.2. What is P(X = 6, Y < 2)? 2.3. What is P(X < 7, Y = 5)? 2.4. Find the marginal distribution of Y. What is fy(1)? 2.5. What is Fy (1)? 2.6. What is E(Y)? 2.7. Find the conditional pmf of Y given X = 8. What is P(Y = 1 | X = 8)? 2.8. What is P(Y = 2 | X = 8)? 2.9. What is E(Y | X = 8)?