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
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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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 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6ab09e2-f11a-4486-af0c-015afafa1dbe%2F953b5fb5-5d80-422d-8218-4b759252569b%2Fdbcbjtl_processed.jpeg&w=3840&q=75)
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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