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Exercise 1 Suppose X1, X2, ... are independent random variables with P{X; = 1} = 7, P{X; = 0} = P{X, = -1} = Let So = 0 and Sn = X1+ . .. + Xn. Let Fn denote the information contained in X1, ..., Xn. 1. Which of these is Sn: martingale, submartingale, supermartingale (more than one answer is possible) ? 2. For which values of r is Yn := Sn -rn a martingale? 3. For what u > 1 is it true that if Mn := usn, then Mn is a martingale? For the remainder of this exercise, use this value of u. 4. Is {Mn} a square integrable martingale? 5. Find E 6. Find ELS? | Fs] E[M2 | Fs]