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The random variables X and Y have joint pmf p(x, y) Y =0 Y=1 Y=2 Y=3 X =0 1/8 1/8 0 OO X =1 0

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The random variables X and Y have joint pmf p(x, y) Y =0 Y=1 Y=2 Y=3 X =0 1/8 1/8 0 OO X =1 0 2/8 2/8 X =2 0 0 1/8 1/8 (a) Calculate the marginals for X and Y. Answer We have TH 3200: PROBABILITY THEORY - Page 3 of 4 0 1 2 y 0 1 2 3 Px (2) 2/8 4/8 2/8 PY ( y) 1/8 3/8 3/8 1/8 (b) Calculate E(Y X = x) and V(Y|X = x)

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