4. A parking garage at UNM has installed an automatic gate. Unfortunately, the drivers have a probability of p of crashing into the gate, in which case it needs to be replaced. Also, if the gate has survived m days without a crash, it still must be replaced because of wear-and-tear. What is the long-term expected frequency of gate replacements Hint: Let the states of the Markov chain denote the number of days the gate has survived. Therefore, they should be a total of m+1 states. Finally, the long-term frequency of gate replacements is equal to the long-term expected frequency of visits to state 0.

4. A parking garage at UNM has installed an automatic gate. Unfortunately, the drivers have a probability of p of crashing into the gate, in which case it needs to be replaced. Also, if the gate has survived m days without a crash, it still must be replaced because of wear-and-tear. What is the long-term expected frequency of gate replacements Hint: Let the states of the Markov chain denote the number of days the gate has survived. Therefore, they should be a total of m+1 states. Finally, the long-term frequency of gate replacements is equal to the long-term expected frequency of visits to state 0.

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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