Consider a simple symmetric random walk Sn = ni=1 Xi with S0 = 0 and P(Xi = 1) = P(Xi =1)=0.5foranyi>0. For0

2n1 r P Si=0S2n=2r =n.

i=1

In an election A receives 200 votes while B receivies only 100. Assume that the probability of getting a vote is identical (50%) for A and B. What is the probability that A is always ahead throughout the count?

2. (4pts+3pts) Consider a simple symmetric random walk Sn = _?_ Xi with So = 0 and P(X, = 1) = P(Xi = -1) =0.5 for any i > 0. For 0