(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 0.2. 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 0.2. 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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(i) 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 0.2.
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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