Continuous time markov chains time there is no rst

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Unformatted text preview: (j )p(j, i) q (i, j ) = ⇡ (i) 3.20. Show that chain in Exercise 1.38 with transition probability is 1 2 3 4 1 1/2 2/3 3/4 1 2 3 4 1 /2 0 0 0 1 /3 0 0 0 1/4 0 0 0 is a special case of the age chain. Use this observation and the previous exercise to compute the stationary distribution. 3.21. The city of Ithaca, New York, allows for two-hour parking in all downtown spaces. Methodical parking o cials patrol the downtown area, passing the same point every two hours. When an o cial encounters a car, he marks it with chalk. If the car is still there two hours later, a ticket is written. Suppose that you park your car for a random amount of time that is uniformly distributed on (0, 4) hours. What is the probability you will get a ticket? 3.22. Each time the frozen yogurt machine at the mall breaks down, it is replaced by a new one of the same type. (a) What is the limiting age distribution for the machine in use if the lifetime of a machine has a gamma(2, ) distribution, i.e., the sum of two exponentials with mean...
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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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