In small-town, there are three different types of weather conditions: a sunny day, rainy day, and windy day. A sunny day never happens two days in a row. If it is a sunny day, it is as likely to have a rainy day or windy day the next day. If it is a windy day or rainy day, it has an even chance of having the same conditions the next day. For the other 50%, it is two times more likely to have a bad weather condition than a sunny day. Draw a transition diagram.Is it an ergodic Markov chain (support your answer)?Obtain a transition probability matrix.What is the probability of having a sunny day 2 days from now, if today is a rainy day (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)?What is the probability of having sunny 4 days from now, if today is a rainy day?What is the probability of having a rainy day 3 days from now if today is a windy day?Obtain the mean first passage time for all states.

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Answered: In small-town, there are three…

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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In small-town, there are three different types of weather conditions: a sunny day, rainy day, and windy day. A sunny day never happens two days in a row. If it is a sunny day, it is as likely to have a rainy day or windy day the next day. If it is a windy day or rainy day, it has an even chance of having the same conditions the next day. For the other 50%, it is two times more likely to have a bad weather condition than a sunny day.

Draw a transition diagram.
Is it an ergodic Markov chain (support your answer)?
Obtain a transition probability matrix.
What is the probability of having a sunny day 2 days from now, if today is a rainy day (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)?
What is the probability of having sunny 4 days from now, if today is a rainy day?
What is the probability of having a rainy day 3 days from now if today is a windy day?
Obtain the mean first passage time for all states.

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