Suppose in small town there are three places to eat, one Chinese restaurant, one Mexican restaurant, and a pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of those who eat in Chinese restaurant go to Mexican, 20% eat at home, and 30% go to pizza place next time. From those who eat in Mexican restaurant, 10% go to pizza place, 25% go to Chinese restaurant, and 25% eats at home next time. From those who eat at pizza place 30% eat at home, 30% eat at Chinese and 10% eat at Mexican restaurant next time. Those who eat at home 20% go to Chinese, 25% go to Mexican place, and 30% to pizza place next time. (a) Construct the (one-step) transition matrix? (b) Does this Markov chain have steady-state?
Suppose in small town there are three places to eat, one Chinese restaurant, one Mexican restaurant, and a pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of those who eat in Chinese restaurant go to Mexican, 20% eat at home, and 30% go to pizza place next time. From those who eat in Mexican restaurant, 10% go to pizza place, 25% go to Chinese restaurant, and 25% eats at home next time. From those who eat at pizza place 30% eat at home, 30% eat at Chinese and 10% eat at Mexican restaurant next time. Those who eat at home 20% go to Chinese, 25% go to Mexican place, and 30% to pizza place next time. (a) Construct the (one-step) transition matrix? (b) Does this Markov chain have steady-state?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:6. Suppose in small town there are three places to eat, one Chinese restaurant, one Mexican restaurant, and a
pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of
those who eat in Chinese restaurant go to Mexican, 20% eat at home, and 30% go to pizza place next time.
From those who eat in Mexican restaurant, 10% go to pizza place, 25% go to Chinese restaurant, and 25% eats
at home next time. From those who eat at pizza place 30% eat at home, 30% eat at Chinese and 10% eat at
Mexican restaurant next time. Those who eat at home 20% go to Chinese, 25% go to Mexican place, and 30% to
pizza place next time.
(a) Construct the (one-step) transition matrix?
(b) Does this Markov chain have steady-state?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 11 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON