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. Spe 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 1/6 of the time . if it is cloudy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day 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 1/2 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. Find the proportion of days that have each type of weather in the long run. 000 P-000 000 Sunny Proportion of days that are Cloudy Rainy
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. Spe 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 1/6 of the time . if it is cloudy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day 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 1/2 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. Find the proportion of days that have each type of weather in the long run. 000 P-000 000 Sunny Proportion of days that are Cloudy Rainy
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 1/3 of the time, and be cloudy the next day 1/6 of the time
if it is cloudy on one day, it will be sunny the next day 1/2 of the time, and never be cloudy the next day
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 1/2 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.
Find the proportion of days that have each type of weather in the long run.
000
P-000
000
Sunny
Proportion of days that are Cloudy
Rainy
0
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