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5. (10 points) Let (Z t ) tEN iid random variables on a probability space (2, A, P) with values in {+ 1} and the distribution LP (Z t ) = 2 3 81+ 1 30 -1 . Denote by X = (Xn ) on=. with Xn = > 1= 1 Z t the associated random walk. Calculate the probability for a given a E N '[e- = " X :[u'o]UN = WA pue e = " X : ON = uf] d =: ed (3) that X hits level a at some point without first having hit level -a. Note: One possible solution uses a martingale, which is then suitably is stopped