markov chain inventory transition matrix

Project Description:

1. a company has two machines. during any day, each machine that is working at the beginning of the day has a chance of breaking down. if a machine breaks down during the day, it is sent to a repair facility and will be working two days after it breaks down. (thus, if a machine breaks down during day 3, it will be working at the beginning of day 5.) letting the state of the system be the number of machines working at the beginning of the day, formulate a transition probability matrix for this situation.
suppose a machine that breaks down returns to service three days later (for instance, a machine that breaks down during day 3 would be back in working order at the beginning of day 6). determine a transition probability matrix for this situation.

[note: must have a fully worked solution with proof].
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