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 3/5 of the time, and never be cloudy the next day 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 1/10 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 1/5 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 0 0 0 0 Sunny Proportion of days that are Cloudy = 0 Rainy 0 11
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 3/5 of the time, and never be cloudy the next day 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 1/10 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 1/5 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 0 0 0 0 Sunny Proportion of days that are Cloudy = 0 Rainy 0 11
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 3/5 of the time, and never be cloudy the next day
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 1/10 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 1/5 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
Proportion of days that are Cloudy
Rainy
=
0
0
0
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