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A car wash has two stations, 1 and 2. The service time at station 1 is...

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Basic Math

A car wash has two stations, 1 and 2. The service time atstation 1 is exponentially distributed with parameter ?1, and theservice time at station 2 is exponentially distributed withparameter ?2.When a car arrives at the car wash, it begins serviceat station 1, provided station 1 is free; otherwise, the car waitsuntil station 1 is available. Upon completing service at station 1,the car then proceeds to station 2, provided station 2 is free;otherwise, the car has to wait at station 1, blocking other carsfrom receiving service at station 1. The car exits thecarwash afterservice at station 2 is completed. Different cars are independentof each other, and for any car, the service time at station 1 isindependent of the service time at station 2.When you arrive, thereis only one car at the car wash, and it is receiving service atstation 1.Compute the expected time from your arrival until yourexit from the car wash.

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