Consider a simple symmetric random walk started at k, (0
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Consider a simple symmetric random walk started at k, (0 < k < N), which stops when it first hits either 0 or N. (a) Sho
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Consider a simple symmetric random walk started at k, (0 < k < N), which stops when it first hits either 0 or N. (a) Show that the expected number of visits to j, (0 < j < k), before the walk stops is 2j(N ? k)/N. (b) Find the corresponding expression for k < j < N. (c) Find the distribution of the number of visits X to its starting point k, and show that X is independent of where the walk stops.
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