Consider the set of points in the set C: Suppose that we pick a point (X, Y)

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Consider the set of points in the set C:C = {(x, y) |x, y = Z, x + y  2}.

Suppose that we pick a point (X, Y) from this set completely at random. Thus, each point has a probability of 1/11 of being chosen.

a. Find the joint and marginal PMFs of X and Y.

b. Find the conditional PMF of X given Y = 1.

c. Are X and Y independent?

d. Find E[XY2].

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