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

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

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