Suppose in a small town there are three places to eat, a Chinese restaurant, a 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 the Chinese restaurant go to Mexican next time, 20% eat home and 30% go to the pizza place. From those who eat in the Mexican restaurant, 10% go to the pizza place, 25% go to the Chinese restaurant, and 25% eats at home next time. From those who eat at the pizza place, 30% eat at home, 30% eat at the Chinese restaurant, and 10% eat at the Mexican restaurant next time. Those who eat at home, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% to the pizza place. a. Set us the matrix of transition probabilities and show the transition diagram b. Find the steady state probabilities c. In the long run, which restaurant will have the most customer

Suppose in a small town there are three places to eat, a Chinese restaurant, a 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 the Chinese restaurant go to Mexican next time, 20% eat home and 30% go to the pizza place. From those who eat in the Mexican restaurant, 10% go to the pizza place, 25% go to the Chinese restaurant, and 25% eats at home next time. From those who eat at the pizza place, 30% eat at home, 30% eat at the Chinese restaurant, and 10% eat at the Mexican restaurant next time. Those who eat at home, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% to the pizza place. a. Set us the matrix of transition probabilities and show the transition diagram b. Find the steady state probabilities c. In the long run, which restaurant will have the most customer

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...

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Suppose in a small town there are three places to eat, a Chineserestaurant, a Mexican restaurant, and a pizza place. Everyone in town eats dinnerin one of these places or has dinner at home. Assume that 20% of those who eat inthe Chinese restaurant go to Mexican next time, 20% eat home and 30% go to thepizza place. From those who eat in the Mexican restaurant, 10% go to the pizzaplace, 25% go to the Chinese restaurant, and 25% eats at home next time. Fromthose who eat at the pizza place, 30% eat at home, 30% eat at the Chineserestaurant, and 10% eat at the Mexican restaurant next time. Those who eat athome, 20% go to the Chinese restaurant, 25% go to Mexican restaurant, and 30% tothe pizza place. a. Set us the matrix of transition probabilities and show the transition b. Find the steady state probabilities c. In the long run, which restaurant will have the most customer