Question: Consider three random variables X, Y, and Z. Suppose that Y takes on k val- ues y.....y, that X takes on values x....,x, and that

Consider three random variables X, Y, and Z. Suppose that Y takes on k val- ues y.....y, that X takes on values x....,x, and that Z takes on m val- ues ... The joint probability distribution of X, Y, Z is Pr(X=x, Y= y,Z=2), and the conditional probability distribution of Y given X and Z is Pr(YyX x,Z= 2) = P(x-12-1)

a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution. [Hint: This is a generalization of Equation (2.16).]

b. Show that E(Y) =E[E(YX,Z)]. [Hint: This is a generalization of Equations (2.19) and (2.20).]

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