question archive A postman delivers mail to all houses in a neighborhood whose layout is given in Figure 1

A postman delivers mail to all houses in a neighborhood whose layout is given in Figure 1

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A postman delivers mail to all houses in a neighborhood whose layout is given in Figure 1. The intersections are numbered 1 through 6 and every line segment between two intersections denotes a possible road (e .g. 1 -) 2, 2 —) 5 etc.). In order to break the monotony of his daily routine, the postman does the following: every time he arrives at an intersection along a particular road, he takes one of the remaining roads available to him with equal probability (e .g. if he arrives at intersection 5 along 2 -) 5, he then takes either 5 —) 4 or 5 -> 6 with probability 1/2). I) Model the postman’s choice of route as a DTMC, making sure to clearly de?ne your states. 11) Cornpute the limiting distribution of the DTMC . III) What fraction of the time dues the postman take a road that has intersection 5 as one of its endpoints? 

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