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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.
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
- Spring '10
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