23.33 Suppose that the weather in Ann Arbor in July can be characterized as sunny, rainy, or cloudy (with no rain). By looking up back issues of the Ann Arbor News, we estimate that if it is sunny on a July day, it is equally likely to be sunny or cloudy on the next day, but it won't rain. If a July day is cloudy, there is a 50 percent chance that it will rain on the next day, a 25 percent chance that it will be sunny, and a 25 percent chance that it will remain cloudy without rain. If it rains on a July day, it won't be sunny the next day, and there is a 50-50 chance of continued rain. a) Write out the corresponding Markov system. b) Show that the underlying matrix is regular. c) What is the long-run distribution of weathers for July dates? d) Write out the general solution of the underlying system of difference equations.

23.33 Suppose that the weather in Ann Arbor in July can be characterized as sunny, rainy, or cloudy (with no rain). By looking up back issues of the Ann Arbor News, we estimate that if it is sunny on a July day, it is equally likely to be sunny or cloudy on the next day, but it won't rain. If a July day is cloudy, there is a 50 percent chance that it will rain on the next day, a 25 percent chance that it will be sunny, and a 25 percent chance that it will remain cloudy without rain. If it rains on a July day, it won't be sunny the next day, and there is a 50-50 chance of continued rain. a) Write out the corresponding Markov system. b) Show that the underlying matrix is regular. c) What is the long-run distribution of weathers for July dates? d) Write out the general solution of the underlying system of difference equations.

Name: Could you please help with a and b? 23.33 Suppose that the weather in
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Description: Could you please help with a and b? 23.33 Suppose that the weather in Ann Arbor in July can be characterized as sunny, rainy,or cloudy (with no rain). By looking up back issues of the Ann Arbor News, weestimate that if it is sunny on a July day, it i

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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