Question: 5.2. Let U,, U2, . . . be independent random variables each uniformly distributed over the interval (0, 1]. Show that X0 = 1 and

5.2. Let U,, U2, . . . be independent random variables each uniformly distributed over the interval (0, 1]. Show that X0 = 1 and X,, = 2"U, U for n = 1, 2.... defines a martingale.

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