B.10. The following table gives the joint PDF of random variables X and Y, where X = the first-year rate of return (%) expected from investment A, and Y = the first-year rate of return (%) expected from investment B. RATES OF RETURN ON TWO INVESTMENTS TABLE B-5 X(%) Y(%) -10 0 20 30 20 50 0.27 0.00 0.08 0.04 0.16 0.10 0.00 0.35 APPENDIX B: CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS 459 a. Find the marginal distributions of Y and X. b. Calculate the expected rate of return from investment B. c. Find the conditional distribution of Y, given X = 20. d. Are X and Y independent random variables? How do you know? Hint: 4 2 E(XY) X;Y; f(X;, Y;) , X1Y=1 B.10. The following table gives the joint PDF of random variables X and Y, where X = the first-year rate of return (%) expected from investment A, and Y = the first-year rate of return (%) expected from investment B. RATES OF RETURN ON TWO INVESTMENTS TABLE B-5 X(%) Y(%) -10 0 20 30 20 50 0.27 0.00 0.08 0.04 0.16 0.10 0.00 0.35 APPENDIX B: CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS 459 a. Find the marginal distributions of Y and X. b. Calculate the expected rate of return from investment B. c. Find the conditional distribution of Y, given X = 20. d. Are X and Y independent random variables? How do you know? Hint: 4 2 E(XY) X;Y; f(X;, Y;) , X1Y=1