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 p.m.f. of X and Y on the space of X and Y.

b) Compute the marginal p.m.f.'s.

c) Are X and Y independent? Why or why not?

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