Select an (even) integer randomly from the set {0, 2, 4, 6, 8}. Then select an integer

Question:

Select an (even) integer randomly from the set {0, 2, 4, 6, 8}. Then select an integer randomly from the set {0, 1, 2, 3, 4}. Let X equal the integer that is selected from the first set and let Y equal the sum of the two integers.
(a) Show the joint pmf of X and Y on the space of X and Y.
(b) Compute the marginal pmfs.
(c) Are X and Y independent? Why or why not?