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(d) Compute the stable matrix for the above process. (e) In the long term, what is the probability that, on a given day, the wind speed is medium?

(d) Compute the stable matrix for the above process. (e) In the long term, what is the probability that, on a given day, the wind speed is medium?

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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can you please do part d and e , please provide explanations 

5. The wind speed next to a wind turbine is measured at 9am each morning. The possible wind speeds are divided into fast, medium and slow. It has been observed that the wind speed is a Markov process. If the speed is high on a given day, it will be high on the following day with a probability of 0.4, medium with a probability of 0.5, and low with a probability of 0.1. If it is medium on a given day, it will be never be high on the following day, but it will be medium with a probability of 0.3 and low with a probability of 0.7. If it is low on a given day, it will be high on the following day with a probability of 0.3, medium with a probability of 0.1 and low with a probability of 0.6. (a) Write down the transition matrix, A, for the above process. (b) Show that the transition matrix A in part (a) is regular. (c) Suppose the wind speed is high on Day 1. Compute the probability that the wind speed is low on Day 3. (d) Compute the stable matrix for the above process. (e) In the long term, what is the probability that, on a given day, the wind speed is medium?
Transcribed Image Text:5. The wind speed next to a wind turbine is measured at 9am each morning. The possible wind speeds are divided into fast, medium and slow. It has been observed that the wind speed is a Markov process. If the speed is high on a given day, it will be high on the following day with a probability of 0.4, medium with a probability of 0.5, and low with a probability of 0.1. If it is medium on a given day, it will be never be high on the following day, but it will be medium with a probability of 0.3 and low with a probability of 0.7. If it is low on a given day, it will be high on the following day with a probability of 0.3, medium with a probability of 0.1 and low with a probability of 0.6. (a) Write down the transition matrix, A, for the above process. (b) Show that the transition matrix A in part (a) is regular. (c) Suppose the wind speed is high on Day 1. Compute the probability that the wind speed is low on Day 3. (d) Compute the stable matrix for the above process. (e) In the long term, what is the probability that, on a given day, the wind speed is medium?
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