Suppose that the k th investment leads to an interest

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Unformatted text preview: t takes the policeman an average of 5 minutes to write such a ticket. The other 10% of the stops are for more serious o↵enses, leading to an average fine of $300. These more serious charges take an average of 30 minutes to process. In the long run, at what rate (in dollars per minute) does he assign fines. 3.8. Counter processes. As in Example 1.5, we suppose that arrivals at a counter come at times of a Poisson process with rate . An arriving particle that finds the counter free gets registered and then locks the counter for an amount of time ⌧ . Particles that arrive while the counter is locked have no e↵ect. (a) Find the limiting probability the counter is locked at time t. (b) Compute the limiting fraction of particles that get registered. 3.9. A cocaine dealer is standing on a street corner. Customers arrive at times of a Poisson process with rate . The customer and the dealer then disappear from the street for an amount of time with distribution G while the transaction is completed. Customers tha...
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