onent per day. Each repairman successfully fixes the component with probability 70% regardless of whether he has worked on it previous days. Model the system as a Markov chain Write down equations for determining lon

onent per day. Each repairman successfully fixes the component with probability 70% regardless of whether he has worked on it previous days. Model the system as a Markov chain Write down equations for determining lon

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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Question

A system consists of five components, each can be operational or not. Each day one operational component is used and it will fail with probability 20%. Suppose there are five repairmen available that can each work on one broken down component per day. Each repairman successfully fixes the component with probability 70% regardless of whether he has worked on it previous days.

Model the system as a Markov chain

Write down equations for determining long-run proportions.

Suppose that you are interested in the average number of repairmen who are working per day. Explain how you would find it using your model. You are not asked to solve any equations here, instead describe how you would use the solutions.

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