1 (30 points) Let the sample space 0, 1 and the probability on be given by the density p(x) 2x over 0, 1 We define random variables X and Y by 1, 0 w 1 4 0, 1 4w 1 2 X(w) and Y(w) 1, 1 2w 3 4 Y(w) 1, 0 w 1 2 0, 1 2w1 0, 3 4 w1 (a) Find the conditional expectation E(X Y) (b) Show that E(E(X Y)) E(X)

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Question: 1. (30 points) Let the sample space = [0, 1] and the probability on be given by the density p(x) = 2x over [0,

1. (30 points) Let the sample space = [0, 1] and the

1. (30 points) Let the sample space = [0, 1] and the probability on be given by the density p(x) = 2x over [0, 1]. We define random variables X and Y by 1, 0 w < 1/4 0, 1/4w

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