Question: Exercise 3.15. We perform a random walk on Z starting from (0, 0). For this let Xn,n 2 1 be i.i.d. random variables so that

Exercise 3.15. We perform a random walk on Z" starting from (0, 0). For this let Xn,n 2 1 be i.i.d. random variables so that X,, is one of (0, 1), (1, 0), (0, -1), (-1,0) with probability equal probabilities. Then S. = > X, is the position of the random walker after the nth step. Let R. denote the distance from the origin after n steps. Show that R2 - n is a martingale

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