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 2/5 of the timeif it is cloudy on one day, it will be sunny the next day 1/5 of the time, and be cloudy the next day 3/10 of the timeif it is rainy on one day, it will be sunny the next day 1/5 of the time, and be cloudy the next day 2/5 of the timeUsing '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.Use your matrix to determine the probability that it will rain on Tuesday if it is sunny on Sunday.(here's a sample of what the answer would look like) The correct answer is:P =1576 1110 10253131310 50 12 155 10 10Probability of rain on Tuesday = 23/100

We define the three weather states as Sunny (S), Cloudy (C) and Rainy (R)Let the transition matrix P…

Answered: The correct answer is: P = 1576 11 10…

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. Specfically:

if it is sunny on one day, it will never be sunny the next day, and be cloudy the next day 2/5 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 3/10 of the time
if it is rainy on one day, it will be sunny the next day 1/5 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.

Use your matrix to determine the probability that it will rain on Tuesday if it is sunny on Sunday.

(here's a sample of what the answer would look like)