In small town there are three different types of whether conditions: 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 next day. For the other 50%, it is two times more likely to have a bad weather conditions than a sunny day.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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In small town there are three different types of whether conditions: 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 next
day. For the other 50%, it is two times more likely to have a bad weather
conditions than a sunny day.
a) (Calculate without using matrix multiplication, hint: calculate just the
needed value or matrix element)?
b) What is the probability of having sunny 4 days from now, if today is a
rainy day?
c) What is the probability of having a rainy day 3 days from now if today is a
windy day?
d) Obtain the mean first passage time for all states
Transcribed Image Text:In small town there are three different types of whether conditions: 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 next day. For the other 50%, it is two times more likely to have a bad weather conditions than a sunny day. a) (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)? b) What is the probability of having sunny 4 days from now, if today is a rainy day? c) What is the probability of having a rainy day 3 days from now if today is a windy day? d) Obtain the mean first passage time for all states
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Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case you require the unanswered parts also, kindly re-post that parts separately.

From the given information, there are three different types of weather conditions: 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 next day.

For the other 50%, it is two times more likely to have a bad weather conditions than a sunny day.

a.

The transition matrix is,

P=01212161226162612

 

 

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