Let X and Y have the following joint probability function X y 1 2 3 12 3 .1 .1 0 .1 .2 3 .1 .1 0 (a) Find the probabilit

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Let X And Y Have The Following Joint Probability Function X Y 1 2 3 12 3 1 1 0 1 2 3 1 1 0 A Find The Probabilit 1 (148.03 KiB) Viewed 42 times

Let X and Y have the following joint probability function X y 1 2 3 12 3 .1 .1 0 .1 .2 3 .1 .1 0 (a) Find the probability functions for X + Y, XY, X/Y. (b) Using the p.f.'s obtained in (a), find E(X + Y), E(XY), E(X/Y), Var(X + Y). (c) Find the p.f.'s of X and of Y. Determine E(X), E(Y), Var(X) and compare Var(Y). Using the results of (b) and (c), (i) E(X+Y) and E(X) + E(Y) (ii) E(XY) and E(X)E(Y) (iii) E(X/Y) and E(X)/E(Y). (e) Are X and Y independent random variables? Compare Var(X + Y) and Var(X) + Var(Y). Comment on this result.