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A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impos- sible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.

A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impos- sible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.

A First Course in Probability (10th Edition)
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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A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impos- sible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.
Transcribed Image Text:A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impos- sible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.
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