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 1/5 of the time, and be cloudy the next day 1/5 of the time • if it is cloudy on one day, it will be sunny the next day 3/10 of the time, and be cloudy the next day 3/10 of the time • if it is rainy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day 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 Tuesday if it is sunny on Sunday. 000 P=000 000 Probability of rain on Tuesday = 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 1/5 of the time, and be cloudy the next day 1/5 of the time • if it is cloudy on one day, it will be sunny the next day 3/10 of the time, and be cloudy the next day 3/10 of the time • if it is rainy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day 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 Tuesday if it is sunny on Sunday. 000 P=000 000 Probability of rain on Tuesday = 0
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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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 1/5 of the time, and be cloudy the next day 1/5 of the time
• if it is cloudy on one day, it will be sunny the next day 3/10 of the time, and be cloudy the next day 3/10 of the time
• if it is rainy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day
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 Tuesday if it is sunny on Sunday.
000
P=000
000
Probability of rain on Tuesday 0
=
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