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The weather on any given day in a particular city can be sunny, cloudy, or rainy. It ha 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 be sunny the next day 1/5 of the time, and be cl next day 2/5 of the time • if it is cloudy on one day, it will be sunny the next day 3/5 of the time, and neve cloudy the next day • if it is rainy on one day, it will be sunny the next day 1/5 of the time, and be clo next day 2/5 of the time Using 'sunny' 'cloudy' and 'rainy' (in that order) as the states in a system set up the

The weather on any given day in a particular city can be sunny, cloudy, or rainy. It ha 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 be sunny the next day 1/5 of the time, and be cl next day 2/5 of the time • if it is cloudy on one day, it will be sunny the next day 3/5 of the time, and neve cloudy the next day • if it is rainy on one day, it will be sunny the next day 1/5 of the time, and be clo next day 2/5 of the time Using 'sunny' 'cloudy' and 'rainy' (in that order) as the states in a system set up the

A First Course in Probability (10th Edition)
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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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 be sunny the next day 1/5 of the time, 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 3/5 of the time, and never be cloudy the next day • 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. 000 P=000 000 Probability of rain on Tuesday = 0
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 be sunny the next day 1/5 of the time, 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 3/5 of the time, and never be cloudy the next day • 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. 000 P=000 000 Probability of rain on Tuesday = 0
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