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%. Any time there no operational components at the end of a day, maintenance will be performed and all non-operational components will be repaired (with probability 1). The system does not perform any other tasks on the day of repairs. 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 days that the system is under repair. Explain how you would find it using your model.

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