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Ef(X)g(Y )1 A = E f(X)Eg(Y ) A1 A It follows from the definition of conditional expectation that Ef(X)g(Y ) A = E f(X)Eg(Y ) A A = Ef(Y ) AEg(Y ) A, so X and Y are independent conditionally on A D Exercise 2 Let X = (X n) n≥0 be a martingale (1) Suppose that T is a stopping time, show that X T is also a martingaleDepartment of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the US

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