2.19 Consider two random variables X and Y. Suppose that Y takes on k values y1,

c, yk and that X takes on l values x1,

c, xl.

a. Show that Pr(Y = yj) = gli

= 1Pr(Y = yj  X = xi) Pr(X = xi). [Hint:

Use the definition of Pr(Y = yj  X = xi).]

b. Use your answer to

(a) to verify Equation (2.19).

c. Suppose that X and Y are independent. Show that sXY = 0 and corr(X, Y) = 0.