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).