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Consumers in Shelbyville have a choice of one of two fast food restaurants, Krusty's and McDonald's. Both have trouble keeping customers. Of those who last went to Krusty's, 55% will go to McDonald's next time, and of those who last went to McDonald's, 80% will go to Krusty's next time. (a) Find the transition matrix describing this situation. 0.45 0.8 0.55 0.2 (b) A customer goes out for fast food every Sunday, and just went to Krusty's. i. What is the probability that two Sundays from now she will go to McDonald's? 0.3575 ii. What is the probability that three Sundays from now she will go to McDonald's? 0.4249 (c) Suppose a consumer has just moved to Shelbyville, and there is a 40% chance that he will go to Krusty's for his first fast food outing. What is the probability that his third fast food experience will be at Krusty's? 0.4

Consumers in Shelbyville have a choice of one of two fast food restaurants, Krusty's and McDonald's. Both have trouble keeping customers. Of those who last went to Krusty's, 55% will go to McDonald's next time, and of those who last went to McDonald's, 80% will go to Krusty's next time. (a) Find the transition matrix describing this situation. 0.45 0.8 0.55 0.2 (b) A customer goes out for fast food every Sunday, and just went to Krusty's. i. What is the probability that two Sundays from now she will go to McDonald's? 0.3575 ii. What is the probability that three Sundays from now she will go to McDonald's? 0.4249 (c) Suppose a consumer has just moved to Shelbyville, and there is a 40% chance that he will go to Krusty's for his first fast food outing. What is the probability that his third fast food experience will be at Krusty's? 0.4

Advanced Engineering Mathematics
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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Consumers in Shelbyville have a choice of one of two fast food restaurants, Krusty's and McDonald's. Both have trouble keeping customers. Of those who last went to Krusty's, 55% will go to McDonald's next time, and of those who last went to McDonald's, 80% will go to Krusty's next time. (a) Find the transition matrix describing this situation. 0.45 0.55 0.2 (b) A customer goes out for fast food every Sunday, and just went to Krusty's. i. What is the probability that two Sundays from now she will go to McDonald's? 0.3575 (d) Find the steady-state vector. 0.8 ii. What is the probability that three Sundays from now she will go to McDonald's? 0.4249 (c) Suppose a consumer has just moved to Shelbyville, and there is a 40% chance that he will go to Krusty's for his first fast food outing. What is the probability that his third fast food experience will be at Krusty's? 0.4 0.6 0.4
Transcribed Image Text:Consumers in Shelbyville have a choice of one of two fast food restaurants, Krusty's and McDonald's. Both have trouble keeping customers. Of those who last went to Krusty's, 55% will go to McDonald's next time, and of those who last went to McDonald's, 80% will go to Krusty's next time. (a) Find the transition matrix describing this situation. 0.45 0.55 0.2 (b) A customer goes out for fast food every Sunday, and just went to Krusty's. i. What is the probability that two Sundays from now she will go to McDonald's? 0.3575 (d) Find the steady-state vector. 0.8 ii. What is the probability that three Sundays from now she will go to McDonald's? 0.4249 (c) Suppose a consumer has just moved to Shelbyville, and there is a 40% chance that he will go to Krusty's for his first fast food outing. What is the probability that his third fast food experience will be at Krusty's? 0.4 0.6 0.4
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