Let X and Y have the following joint distribution: X \Y  0 1 2     0   2/12  1/12  5/12     1   1/12  1/12  2/12 (a) Find the probability distribution of X|Y = 0, and E[X|Y = 0]. (b) Find E[Y ] and E[X]. (c) Find the probability that Y is larger than zero. (d) Are X and Y dependent? Justify your answer

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