Consider a random walk on {0, ..., k}, which moves left and right with respec- tive probabilities q and p. If the walk is at 0 it transitions to 1 on the next step. If the walk is at k it transitions to k – 1 on the next step. This is called random walk with reflecting boundaries. Assume that k = 3, q = 1/4, p = 3/4, and the initial distribution is uniform. For the following, use technology if needed. 1p. (a) Exhibit the transition matrix.

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Chapter1: Combinatorial Analysis
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Consider a random walk on {0, ..., k}, which moves left and right with respec-
tive probabilities q and p. If the walk is at 0 it transitions to 1 on the next step.
If the walk is at k it transitions to k – 1 on the next step. This is called random
walk with reflecting boundaries. Assume that k = 3, q = 1/4, p = 3/4, and the
initial distribution is uniform. For the following, use technology if needed.
1p.
(a) Exhibit the transition matrix.
Transcribed Image Text:Consider a random walk on {0, ..., k}, which moves left and right with respec- tive probabilities q and p. If the walk is at 0 it transitions to 1 on the next step. If the walk is at k it transitions to k – 1 on the next step. This is called random walk with reflecting boundaries. Assume that k = 3, q = 1/4, p = 3/4, and the initial distribution is uniform. For the following, use technology if needed. 1p. (a) Exhibit the transition matrix.
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