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Unformatted text preview: ndependent. What is the long-run fraction of time that it rains? 3.2. Monica works on a temporary basis. The mean length of each job she gets is 11 months. If the amount of time she spends between jobs is exponential with mean 3 months, then in the long run what fraction of the time does she spend working? 114 CHAPTER 3. RENEWAL PROCESSES 3.3. Thousands of people are going to a Grateful dead concert in Pauley Pavillion at UCLA. They park their 10 foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on (0, 10). In the long run, what fraction of the street is covered with cars? 3.4. The times between the arrivals of customers at a taxi stand are independent and have a distribution F with mean µF . Assume an unlimited supply of cabs, such as might occur at an airport. Suppose that each customer pays a random fare with distribution G and mean µG . Let W (t) be the total fares paid up to time t. Find limt!1 E W (t)/t. 3.5...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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