Let's consider a supermarket with three cash registers. The operation of the cash registers is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs. The probability of a working cash register breaking down is 1/5, and the probability of a cash register undergoing repair becoming operational is 3/5. The processes of breakdown and repair of cash registers are independent of each other. 1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition probability matrix. 2. (15 pts) What is the long-run proportion of days when none of the cash registers are operational?
Let's consider a supermarket with three cash registers. The operation of the cash registers is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs. The probability of a working cash register breaking down is 1/5, and the probability of a cash register undergoing repair becoming operational is 3/5. The processes of breakdown and repair of cash registers are independent of each other. 1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition probability matrix. 2. (15 pts) What is the long-run proportion of days when none of the cash registers are operational?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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![Let's consider a supermarket with three cash registers. The operation of the cash registers
is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs.
The probability of a working cash register breaking down is 1/5, and the probability of a
cash register undergoing repair becoming operational is 3/5. The processes of breakdown
and repair of cash registers are independent of each other.
1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition
probability matrix.
2. (15 pts) What is the long-run proportion of days when none of the cash registers are
operational?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c93124a-e14b-4c92-8ceb-22696b8e96ab%2Fb557e44c-4646-45af-a707-fdb623edd1a7%2Fn4lyl5i_processed.png&w=3840&q=75)
Transcribed Image Text:Let's consider a supermarket with three cash registers. The operation of the cash registers
is checked daily, and if a register is found to be faulty, it is sent to the workshop for repairs.
The probability of a working cash register breaking down is 1/5, and the probability of a
cash register undergoing repair becoming operational is 3/5. The processes of breakdown
and repair of cash registers are independent of each other.
1. (25 pts) Model this problem using a discrete time Markov chain. Present the transition
probability matrix.
2. (15 pts) What is the long-run proportion of days when none of the cash registers are
operational?
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