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 never be sunny the next day, and be cloudy the next day 4/5 of the time • if it is cloudy 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 rainy on one day, it will be sunny the next day 2/5 of the time, and be cloudy the next day 2/5 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. Find the proportion of days that have each type of weather in the long run. 000 P=000 000 Sunny 0 Proportion of days that are Cloudy 0 Rainy 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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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 never be sunny the next day, and be cloudy the next day
4/5 of the time
• if it is cloudy 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 rainy on one day, it will be sunny the next day 2/5 of the time, and be cloudy the
next day 2/5 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.
Find the proportion of days that have each type of weather in the long run.
000
P=000
000
Sunny 0
0
0
Proportion of days that are Cloudy
Rainy
=
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 never be sunny the next day, and be cloudy the next day 4/5 of the time • if it is cloudy 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 rainy on one day, it will be sunny the next day 2/5 of the time, and be cloudy the next day 2/5 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. Find the proportion of days that have each type of weather in the long run. 000 P=000 000 Sunny 0 0 0 Proportion of days that are Cloudy Rainy =
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