Question: 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

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 Pr1Y = yj2 = gl i = 1Pr1Y = yj X = xi2 Pr1X = xi2. [Hint:

Use the definition of Pr1Y = yj X = xi2.]

b. Use your answer to

(a) to verify Equation (2.19).

c. Suppose that X and Y are independent. Show that sXY = 0 and corr1X, Y2 = 0.

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