factory worker will quit with probability 1⁄2 during her first month, with probability 1⁄4 during her second month and with probability 1/8 each month after that. Whenever someone quits, their replacement will start at the beginning of the next month and follow the same pattern. Model this position’s status as a Markov chain. What is the long-run probability of having a new employee on a given month? please provide steps and explanations for answers

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
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A factory worker will quit with probability 1⁄2 during her first month, with probability 1⁄4 during her second month and with probability 1/8 each month after that. Whenever someone quits, their replacement will start at the beginning of the next month and follow the same pattern. Model this position’s status as a Markov chain. What is the long-run probability of having a new employee on a given month?

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