However disturbances such as tree falls or res can

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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...
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