Question: 2. Consider a simple random walk So = 0, S, = >_ &, n 2 1, on 7 := {...,-2, -1, 0, 1, 2, ...},

2. Consider a simple random walk So = 0, S, = >_ &, n 2 1, on 7 := {...,-2, -1, 0, 1, 2, ...}, where {{ } are iid with P($1 = 1) = P($1 = -1) = (1 - P($1 = 0))/2. Show that for any integer b > 0, P( max S; > b) = 2P(S, > b) + P(S, = b)

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