5. Consider a simple random walk on the set {0, 1, 2, ..., N} in which each step is to the right with probability p or to the left with probability q = 1- p. Absorbing barriers are placed at 0 and N. Show that the number X of positive steps of the walk before absorption satisfies E(X) = {Dk-k+ N(1 − Pk)} where D is the mean number of steps until absorption and pk is the probability of absorption at 0.
5. Consider a simple random walk on the set {0, 1, 2, ..., N} in which each step is to the right with probability p or to the left with probability q = 1- p. Absorbing barriers are placed at 0 and N. Show that the number X of positive steps of the walk before absorption satisfies E(X) = {Dk-k+ N(1 − Pk)} where D is the mean number of steps until absorption and pk is the probability of absorption at 0.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:5. Consider a simple random walk on the set {0, 1, 2, ..., N} in which each step is to the right with
probability p or to the left with probability q = 1- p. Absorbing barriers are placed at 0 and N.
Show that the number X of positive steps of the walk before absorption satisfies
E(X) = {Dk-k+ N(1 − Pk)}
where Dk is the mean number of steps until absorption and pk is the probability of absorption at 0.
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