Let (X, Y) be a bivariate discrete random variable with joint probability mass function specified as: 1 p(2,0) 1 p(0, 0) 12 p(0, 1) 6' Р(1,0) 6' 5 p(2, 1) = p(1,2) 3' 12 6. For all other (x, y) pairs, the joint probability mass function p(x, y) = 0. (a) Compute the correlation between X and Y. (b) Are X and Y independent? Justify your answer mathematically. (c) Find the conditional distribution ofY when X = 1 (d) Compute the conditional variance of Y when X = 1. (e) Verify the formula E(Y) = E[E(Y|X)] for this example by computing the left hand side and the right hand side, and showing the two are equal. %3D

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