EBK FINITE MATHEMATICS & ITS APPLICATIO
12th Edition
ISBN: 8220103677936
Author: HAIR
Publisher: YUZU
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Chapter 8.2, Problem 24E
Weather Patterns The day-to-day changes in weather for a certain part of the country form a Markov process. Each day is sunny, cloudy, or rainy. If it is sunny one day, there is a 70% chance that it will be sunny the following day, a 20% chance that it will be cloudy, and a 10% chance of rain. If it is cloudy one day, there is a 30% chance that it will be sunny the following day, a 50% chance that it will be cloudy, and a 20% chance of rain. If it rains one day, there is a 60% chance that it will be sunny the following day, a 20% chance that it will be cloudy, and a 20% chance of rain. In the long run, what is the daily likelihood of rain?
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardCAPSTONE Explain how to find the nth state matrix of a Markov chain. Explain how to find the steady state matrix of a Markov chain. What is a regular Markov chain? What is an absorbing Markov chain? How is an absorbing Markov chain different than a regular Markov chain?arrow_forwardAbsorbing Markov Chains In Exercises 3740, determine whether the Markov chain with matrix of transition probabilities P is absorbing. Explain. P=[251500153501225151000012]arrow_forward
- Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]arrow_forwardMarkov Chain with Reflecting Boundaries The figure below illustrates an example of a Markov chain with reflecting boundaries. Explain why it is appropriate to say that this type of Markov chain has reflecting boundaries. Use the figure to write the matrix of transition probabilities P for the Markov chain. Find P30 and P31. Find several other high even power 2n and odd powers 2n+1. What do you observe? Find the steady state matrix X of the Markov chain. How are the entries in the column of P2n and P2n+1 related to the entries in X?arrow_forward
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