A certain person goes for a run each morning. When he leaves the 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 3 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 barefoot. We are interested in determining the proportion of time that he runs barefoot. 1. Set this problem up as a discrete time Markov chain. Give the states and the one-step transition probability matrix. 2. Determine the proportion of days that he runs barefoot.

A certain person goes for a run each morning. When he leaves the 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 3 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 barefoot. We are interested in determining the proportion of time that he runs barefoot. 1. Set this problem up as a discrete time Markov chain. Give the states and the one-step transition probability matrix. 2. Determine the proportion of days that he runs barefoot.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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