Ray Cahnman is the proud owner of a 1955 sports car. On any given day, Ray never knows whether his car will start. Ninety percent of the time it would start if it started the previous morning, and 70% of the time it will not start if it did not start the previous morning. Construct the matrix of transition probabilities. What is the probability that it would start tomorrow if it started today? What is the probability that it will start tomorrow if it did not start today?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
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Ray Cahnman is the proud owner of a 1955 sports car. On any given day, Ray never knows whether his car will start. Ninety percent of the time it would start if it started the previous morning, and 70% of the time it will not start if it did not start the previous morning.

  1. Construct the matrix of transition probabilities.
  2. What is the probability that it would start tomorrow if it started today?
  3. What is the probability that it will start tomorrow if it did not start today?
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