Please help with the question attached in the picture below:

6. Let X and Y be discrete random variables with the following probability distribution. 0 2 3 0 0.10 0.05 0.03 0.03 X 1 0.18 0.06 0.06 0.07 2 0.16 0.07 0.08 0.05 3 0.02 0.02 0.01 0.01 (a) Verify that this is a valid probability mass distribution. (b) Calculate P(X 2 2, Y 2 2). (c) Calculate P(X = Y). (d) Find the marginal distribution of X. (e) Calculate E[X]. (f) Calculate E[X|Y = 2]