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

An individual possesses r umbrellas that he employs in going from his home to office, and vice versa. If he is at home (the office) at the beginning (end) of a day and it is raining, then he will take an umbrella with him to the office (home), provided there is 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 for each trip.

(b) Determine the proportion of time that there is no available umbrella to be taken for the trip.

Expert Solution

milcah answered 1 year ago

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