The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been the weather on the previous day. Specfically: • if it is sunny on one day, it will be sunny the next day 2/3 of the time, and be cloudy the • if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and be cloudy th • if it is rainy on one day, it will be sunny the next day 1/6 of the time, and be cloudy the Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transit system. Find the proportion of days that have each type of weather in the long run. 000 P = 0 0 0 000 Sunny 0 Proportion of days that are Cloudy 0 Rainy
The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been the weather on the previous day. Specfically: • if it is sunny on one day, it will be sunny the next day 2/3 of the time, and be cloudy the • if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and be cloudy th • if it is rainy on one day, it will be sunny the next day 1/6 of the time, and be cloudy the Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transit system. Find the proportion of days that have each type of weather in the long run. 000 P = 0 0 0 000 Sunny 0 Proportion of days that are Cloudy 0 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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![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. Specifically:
- If it is sunny on one day, it will be sunny the next day 2/3 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 1/3 of the time, and be cloudy the next day 1/3 of the time.
- 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.
\( P = \begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix} \)
Proportion of days that are
\[
\begin{bmatrix}
\text{Sunny} \\
\text{Cloudy} \\
\text{Rainy}
\end{bmatrix}
=
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2b7ff9-b952-4215-9e0f-f264e2036fb8%2F3c51c24a-2ac5-47ff-b3b1-9022f5a8b341%2Fgscdlxv_processed.png&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. Specifically:
- If it is sunny on one day, it will be sunny the next day 2/3 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 1/3 of the time, and be cloudy the next day 1/3 of the time.
- 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.
\( P = \begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix} \)
Proportion of days that are
\[
\begin{bmatrix}
\text{Sunny} \\
\text{Cloudy} \\
\text{Rainy}
\end{bmatrix}
=
\begin{bmatrix}
0 \\
0 \\
0
\end{bmatrix}
\]
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