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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 Proportion of days that are Cloudy 0 Rainy 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 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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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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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