Question: Problem 4. [4 points | Let (S,),n = 1,2, .. be a symmetric random walk; that is S, = Y |, X; where X; take

Problem 4. [4 points | Let (S,),n = 1,2, .. be a symmetric random walk; that is S, = Y"" |, X; where X; take values 1 and -1 with probabilities % Define Y,, = (1)" cos(wS,,). Show that (Yy,) is a martingale with respect to the filtration generated by the sequence (X, ),n =1,2

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