(1) Let X and Y be independent random variables with distributions 0. 1 2 0 1...

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(1) Let X and Y be independent random variables with distributions 0. 1 2 0 1 3 Pr(X = r) Pr(Y y) Let Z = XY. (i) Find E(Y). (ii) Find Var(Y). (iii) Write down a table giving the probability distribution for Z. (iv) Are the random variables X and Z independent? (1) Let X and Y be independent random variables with distributions 0. 1 2 0 1 3 Pr(X = r) Pr(Y y) Let Z = XY. (i) Find E(Y). (ii) Find Var(Y). (iii) Write down a table giving the probability distribution for Z. (iv) Are the random variables X and Z independent?