1. Let X be a symmetric random walk in dimension 1 with Xo = 0. This...
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1. Let X be a symmetric random walk in dimension 1 with Xo = 0. This means that at each transition, the probability that the process moves one unit to the right is, as is the probability of moving one unit to the left. We have proven in class that X has a single communicating class which is recurrent. This problem seeks to determine lim,- P" for each i. (a) Set up the infinite system of equations to determine 7. (b) If possible, solve this system. (c) Determine both , and kf, the expected return time to state i. 1. Let X be a symmetric random walk in dimension 1 with Xo = 0. This means that at each transition, the probability that the process moves one unit to the right is, as is the probability of moving one unit to the left. We have proven in class that X has a single communicating class which is recurrent. This problem seeks to determine lim,- P" for each i. (a) Set up the infinite system of equations to determine 7. (b) If possible, solve this system. (c) Determine both , and kf, the expected return time to state i.
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To determine the limiting probabilities for each state of the symmetric random walk we can set up an ... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
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