Question: Consider the random walk Sn = X1 + X2 ++ Xn, where the Xi are independent and identically distributed Bernoulli random variables that take on

Consider the random walk Sn = X1 + X2 +···+ Xn, where the Xi are independent and identically distributed Bernoulli random variables that take on the value 1 with probability p = 0.6 and the value −1 with probability q = 1 − p = 0.4.

a. Find the probability P[S8 = 0].

b. What value of p maximizes P[S8 = 0]?

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