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

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Consider the set of points in the set C: C = {(x, y)|x, y ∈ Z,x2 +|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 E[X|Y = 1].

b. Find V ar(X|Y = 1).

c. Find E[X||Y | ≤ 1].

d. Find E[X2||Y | ≤ 1].

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