This is from a course related to Stochastic Processes.

Exercise 3.9. Suppose that {Xx : k 2 1} is a sequence of i.i.d. random variables with P(X1 = 1) = P(X1 = -1) = 2. Let Sn = Er_]Xx. Find a degree three polynomial of Sn (with coefficients possibly depending on n) that is a martingale with respect to {Xk : k 2 1}