Alice flips an unbiased coin twice and records the number of heads as X. Then she takes X balls from an urn randomly without replacement. The urn contains 2 red balls and 1 blues balls. Let Y denote the number of red balls she takes. (a) Fill the joint distribution table of p(x, y) of random variables X, Y. (Don't forget to check the probability in the table should sum to 1.) (b) Compute EY Y X | 4 0 1 2 0 1/4 0 0 1 0 2 1/6

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