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#1

*A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold. Pr(X = 0, Y = 0) = 1/6; Pr(X = 1, Y = 0) = 1/12; Pr(X = 1, Y =1) =1/6 Pr(X = 2, Y = 0) = 1/12; Pr(X = 2, Y = 1) = 1/3; Pr(X = 2, Y = 2) = 1/6. What is the variance of X ?*X and Y are independent random variables with common moment generating function M(t) = et /2. Let W = X + Y and Z = Y - X. Determine the joint moment generating function, M(s, t) of W and Z