(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 14EQ
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(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4.
(ii) If volume is low this week then it will be high next week with a probability of 0.1.
Assume that state 1 is high volume and that state 2 is low volume
(1) Find the transition matrix for this Markov process.
(2) If the volume this week is high, what is the probability that the volume will be high two weeks from now?
(3) What is the probability that volume will be high for three consecutive weeks?
Transcribed Image Text:(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?
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