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Let (X n ), n = 1, 2, ... denote a sequence of independent and integrable random variables defined on a probability space (, F,

Let (Xn), n = 1, 2, ... denote a sequence of independent and integrable random variables defined on a probability space (, F, P) and assume that E(Xn) = 1 for all n. If Fn is the -algebra generated by X1, X2, ..., Xn and Yn = X1 ... Xn, show that (Yn, Fn), n = 1, 2, ... is a martingale.

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