Arc sine law for maxima. Consider a symmetric random walk S starting from the origin, and let Mn max{S; : 0 ≤ i ≤n}. Show that, for i = 2k, 2k + 1, the probability that the walk reaches M2n for the first time at time i equals P(S2k = 0)P(S2n-2k = 0). =

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