Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it ismclear today. Also assume that these probabilities do not change if information ismalso provided about the weather before today. (i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather.  (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
icon
Related questions
Question

Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it ismclear today. Also assume that these probabilities do not change if information ismalso provided about the weather before today.

(i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. 

(ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Markov Processes and Markov chain
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning