This preview shows page 1. Sign up to view the full content.
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 twohour 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...
View
Full
Document
This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

Click to edit the document details