However when he has not shaved for 4 days his mother

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Unformatted text preview: g patterns in a certain region determines that the pattern of movement between urban (U), suburban (S), and rural areas (R) is given by the following transition matrix. U U .86 S .05 R .03 S .08 .88 .05 R .06 .07 .92 68 CHAPTER 1. MARKOV CHAINS In the long run what fraction of the population will live in the three areas? 1.34. In a large metropolitan area, commuters either drive alone (A), carpool (C), or take public transportation (T). A study showed that transportation changes according to the following matrix: A C S A .8 .05 .05 C .15 .9 .1 T .05 .05 .85 In the long run what fraction of commuters will use the three types of transportation? 1.35. (a) Three telephone companies A, B , and C compete for customers. Each year customers switch between companies according the followinng transition probability ABC A .75 .05 .20 B .15 .65 .20 C .05 .1 .85 What is the limiting market share for each of these companies? 1.36. A professor has two light bulbs in his garage. When both are burned out, they are replaced, and the next day sta...
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