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Question 6 Let (Xn)nen be independent and identically distributed random variables satisfying P(X,, = 1) = P(X, = -1) = Consider the stochastic process (S)ncN.

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Question 6 Let (Xn)nen be independent and identically distributed random variables satisfying P(X,, = 1) = P(X, = -1) = Consider the stochastic process (S)ncN. defined by So := 10 and for each n 2 1 by Sn := So+ Et Xi. Moreover, define T := inf {n >0: Sn = -5}. Then we have that E[ST] = -5. YES NO Question 7 Let (Xn)neNo be a stochastic process taking values in S := Z, and denote by (Fn)neNo the filtration generated by (Xn)neNo. Then the constant process (Zn)neNo defined by Zn := -20 for all n E No is a martingale with respect to (Fn)neNo- YES NO

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