9.10. A certain person goes for a run each morning. When he leaves his house for his run, he is equally likely to go out either the front or the back door, and similarly, when he returns, he is equally likely to go to either the front or the back door. The runner owns 5 pairs of running shoes, which he takes off after the run at whichever door he happens to be. If there are no shoes at the door from which he leaves to go running, he runs barefooted. We are interested in determining the proportion of time that he runs barefooted. a. Set this problem up as a Markov chain. Give the states and the transition probabilities. b. Determine the proportion of days that he runs barefooted.
9.10. A certain person goes for a run each morning. When he leaves his house for his run, he is equally likely to go out either the front or the back door, and similarly, when he returns, he is equally likely to go to either the front or the back door. The runner owns 5 pairs of running shoes, which he takes off after the run at whichever door he happens to be. If there are no shoes at the door from which he leaves to go running, he runs barefooted. We are interested in determining the proportion of time that he runs barefooted. a. Set this problem up as a Markov chain. Give the states and the transition probabilities. b. Determine the proportion of days that he runs barefooted.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9.10. A certain person goes for a run each morning. When he leaves
his house for his run, he is equally likely to go out either the front or the
back door, and similarly, when he returns, he is equally likely to go to
either the front or the back door. The runner owns 5 pairs of running
shoes, which he takes off after the run at whichever door he happens
to be. If there are no shoes at the door from which he leaves to go
running, he runs barefooted. We are interested in determining the
proportion of time that he runs barefooted.
a. Set this problem up as a Markov chain. Give the states and the
transition probabilities.
b. Determine the proportion of days that he runs barefooted.
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