(1) 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 0.3. The manager estimates that the volume is five times as likely to be high as to be low this week.

College Algebra
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ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...
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(1) 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 0.3.
The manager estimates that the volume is five times as likely to be high as to be low this week.
Assume that state 1 is high volume and that state 2 is low volume.
(Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more
than 4 decimal places).)
(1) Find the transition matrix P for this Markov chain:
P =
...
(2) Find the state vector that represents the manager's estimate
Xo = |
[
...
(3) Using this estimate as the initial state vector, find the state vector for two weeks from now:
X, =
What is the probability that two weeks from now the volume will be high?
Transcribed Image Text:(1) 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 0.3. The manager estimates that the volume is five times as likely to be high as to be low this week. Assume that state 1 is high volume and that state 2 is low volume. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).) (1) Find the transition matrix P for this Markov chain: P = ... (2) Find the state vector that represents the manager's estimate Xo = | [ ... (3) Using this estimate as the initial state vector, find the state vector for two weeks from now: X, = What is the probability that two weeks from now the volume will be high?
(4) Again, using the manager's estimate as the initial state vector, find the state vector for three
weeks from now:
..
X3
=
What is the probability that three weeks from now the volume will be high?
(5) Suppose, contrary to the manager's estimate, that this week the volume is low. How many weeks
must pass before a week comes along in which the probability of high volume is at least 0.3?
...
Transcribed Image Text:(4) Again, using the manager's estimate as the initial state vector, find the state vector for three weeks from now: .. X3 = What is the probability that three weeks from now the volume will be high? (5) Suppose, contrary to the manager's estimate, that this week the volume is low. How many weeks must pass before a week comes along in which the probability of high volume is at least 0.3? ...
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