(1) If volume is high this week, then next week it will be high with a probability of 0.8 and low with a probability of 0.2. (ii) If volume is low this week then it will be high next week with a probability of 0.5. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. P = (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?
(1) If volume is high this week, then next week it will be high with a probability of 0.8 and low with a probability of 0.2. (ii) If volume is low this week then it will be high next week with a probability of 0.5. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. P = (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?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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![(1) If volume is high this week, then next week it will be high with a probability of 0.8 and low with a probability of 0.2.
(ii) If volume is low this week then it will be high next week with a probability of 0.5.
Assume that state 1 is high volume and that state 2 is low volume.
(1) Find the transition matrix for this Markov process.
P =
(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a79c17-bf73-44c3-9503-d2f30f855206%2Fa1bbb3ca-b1c4-4875-9489-7e07080ab149%2Fdcpwtt_processed.png&w=3840&q=75)
Transcribed Image Text:(1) If volume is high this week, then next week it will be high with a probability of 0.8 and low with a probability of 0.2.
(ii) If volume is low this week then it will be high next week with a probability of 0.5.
Assume that state 1 is high volume and that state 2 is low volume.
(1) Find the transition matrix for this Markov process.
P =
(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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