Unformatted text preview: in one year.
P
S
E P
.6
.1
0 S
.4
.6
.2 E
0
.3
.8 What is the limiting fraction of drivers in each of these categories?
1.41. Reﬂecting random walk on the line. Consider the points 1, 2, 3, 4 to be
marked on a straight line. Let Xn be a Markov chain that moves to the right
with probability 2/3 and to the left with probability 1/3, but subject this time
to the rule that if Xn tries to go to the left from 1 or to the right from 4 it
stays put. Find (a) the transition probability for the chain, and (b) the limiting
amount of time the chain spends at each site.
1.42. At the end of a month, a large retail store classiﬁes each of its customer’s
accounts according to current (0), 30–60 days overdue (1), 60–90 days overdue
(2), more than 90 days (3). Their experience indicates that the accounts move
from state to state according to a Markov chain with transition probability
matrix:
0123
0 .9 .1 0 0
1 .8 0 .2 0
2 .5 0 0 .5
3 .1 0 0 .9
In the long run what fraction of the accounts are in each category?
1.43. At t...
View
Full
Document
This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

Click to edit the document details