The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been observed to be predictable largely on the basis of the weather on the previous day. Specfically: • if it is sunny on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time • if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time • if it is rainy on one day, it will be sunny the next day 1/6 of the time, and be cloudy the next day 1/6 of the time Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transition matrix for a Markov chain to describe this system. Use your matrix to determine the probability that it will rain on Wednesday if it is sunny on Sunday.

The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been observed to be predictable largely on the basis of the weather on the previous day. Specfically: • if it is sunny on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time • if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time • if it is rainy on one day, it will be sunny the next day 1/6 of the time, and be cloudy the next day 1/6 of the time Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transition matrix for a Markov chain to describe this system. Use your matrix to determine the probability that it will rain on Wednesday if it is sunny on Sunday.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 33EQ

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