Consider two random variables X and Y. Suppose that Y takes
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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
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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 ) = gl i = 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.
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