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Let {X n } n=0 be independent non-negative random variables with X 0 = 1 and E[X n ] = n , n 1 where

Let {Xn} n=0 be independent non-negative random variables with X0 = 1 and E[Xn] = n, n 1 where 0 < n < . Let M0 = 1 and Mn = cn X1X2 . . . Xn, n 1 where cn are constants. Determine {cn} so that {Mn} is a martingale with respect to {Xn}.

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