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 never be sunny the next day, 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 1/3 of the time, and be cloudy the next day 1/2 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. 000 P=000 000 Probability of rain on Wednesday = 0
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 never be sunny the next day, 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 1/3 of the time, and be cloudy the next day 1/2 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. 000 P=000 000 Probability of rain on Wednesday = 0
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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Transcribed Image Text: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 never be sunny the next day, 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 1/3 of the time, and be cloudy the next day 1/2 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.
000
P=000
000
Probability of rain on Wednesday = 0
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