Question: Let X t = 2 t 1 ... t , where s are independent and take on values 0 and 1

Let X_t = 2_t ξ₁ · ... · ξ_t, where ξ’s are independent and take on values 0 and 1 with equal probabilities. Show that Xt is a martingale. What is E{Xt}? What is limt→∞ Xt?

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