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Properties of a Simple Random Walk with Boundaries

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probability of hitting right wall p
0.5
maximum lattice point n
50
This Demonstration shows several basic properties of random walks on a one-dimensional lattice of points
k=0,1,…,n
. At each step, the probability of moving to the right or left is
p
and
1-p
, respectively; the walk ends when it reaches
k=0
or
n
. As a function of the starting position
k
, we show the probability of the walk ending at the right boundary, and the average number of steps taken during the walk (regardless of which boundary it eventually hits).
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