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An individual possesses r umbrellas that he employs in going from his home to office, and...

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Basic Math

An individual possesses r umbrellas that he employs in goingfrom his home to office, and vice versa. If he is at home (theoffice) at the beginning (end) of a day and it is raining, then hewill take an umbrella with him to the office (home), provided thereis one to be
taken. If it is not raining, then he never takes an umbrella.Assume that, independent of the past, it rains at the beginning(end) of a day with probability p.
(a) Define a Markov chain to model the number of umbrellas foreach trip.
(b) Determine the proportion of time that there is noavailable umbrella to be taken for the trip.

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