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Random Walk in One Dimension
Consider a particle on a line that at each time step moves either one unit to the left or one unit to the right. The choice of direction is independent of any prior steps. The probability of moving right at any time is r. The probability of moving left at any time is 1-r. We would like to know for various values of r the probability that a particle will eventually go k steps to the left of its starting position.
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