= 2. Consider a K + 1 dimensional discrete random vector (Y, X) where Y is a scalar random variable and X is a K dimensional random vector. Y takes on values yj, 1, ..., J and X takes on values Xm, m 1, ..., M, respectively, where (Y, X) = (yj, Xm) with probability Pjm for j 1, ..., J and M. = (a) What is the (marginal) distributions of Y and X, respectively? (b) Describe the random variable E(Y|X). (c) In this example, show that E(Y) = E(E(Y|X)). = 2. Consider a K + 1 dimensional discrete random vector (Y, X) where Y is a scalar random variable and X is a K dimensional random vector. Y takes on values yj, 1, ..., J and X takes on values Xm, m 1, ..., M, respectively, where (Y, X) = (yj, Xm) with probability Pjm for j 1, ..., J and M. = (a) What is the (marginal) distributions of Y and X, respectively? (b) Describe the random variable E(Y|X). (c) In this example, show that E(Y) = E(E(Y|X))