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Two supermarkets serving the Northside area of San Antonio, H.E.D. and Walbart, are interested in identifying the habits of their customers in terms of returning back to the store in consecutive weeks. It is found that if a customer shopped at H.E.D. in a given week, the probability that the customer returns to H.E.D. next week is 0.87 and the probability that the customer goes to Walbart is 0.13. If a customer shopped at Walbart in a given week, the probability that the customer returns to Walbart next week is 0.75 and the probability that the customer goes to H.E.D. the next week is 0.25. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at H.E.D. and a 0.5 probability that the customer shopped at Walbart at period 0; that is, n¡(0) = 0.5 and T2(0) = 0.5. Given these initial state probabilities, answer the following questions (round to three decimal places): a. The probability that the consumer shops at H.E.D. in Period 2 =

Two supermarkets serving the Northside area of San Antonio, H.E.D. and Walbart, are interested in identifying the habits of their customers in terms of returning back to the store in consecutive weeks. It is found that if a customer shopped at H.E.D. in a given week, the probability that the customer returns to H.E.D. next week is 0.87 and the probability that the customer goes to Walbart is 0.13. If a customer shopped at Walbart in a given week, the probability that the customer returns to Walbart next week is 0.75 and the probability that the customer goes to H.E.D. the next week is 0.25. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at H.E.D. and a 0.5 probability that the customer shopped at Walbart at period 0; that is, n¡(0) = 0.5 and T2(0) = 0.5. Given these initial state probabilities, answer the following questions (round to three decimal places): a. The probability that the consumer shops at H.E.D. in Period 2 =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Two supermarkets serving the Northside area of San Antonio, H.E.D. and Walbart, are interested in identifying the habits of their customers in terms of returning back to the store in consecutive weeks. It is found that if a customer shopped at H.E.D. in a given week, the probability that the customer returns to H.E.D. next week is 0.87 and the probability that the customer goes to Walbart is 0.13. If a customer shopped at Walbart in a given week, the probability that the customer returns to Walbart next week is 0.75 and the probability that the customer goes to H.E.D. the next week is 0.25. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at H.E.D. and a 0.5 probability that the customer shopped at Walbart at period 0; that is, a1(0) = 0.5 and T2(0) = 0.5. Given these initial state probabilities, answer the following questions (round to three decimal places): a. The probability that the consumer shops at H.E.D. in Period 2 = b. The probability that the consumer shops at Walbart in Period 6 = c. What is the long-run probability (or market share) of H.E.D? d. What is the long-run probability (or market share of Walbart?
Transcribed Image Text:Two supermarkets serving the Northside area of San Antonio, H.E.D. and Walbart, are interested in identifying the habits of their customers in terms of returning back to the store in consecutive weeks. It is found that if a customer shopped at H.E.D. in a given week, the probability that the customer returns to H.E.D. next week is 0.87 and the probability that the customer goes to Walbart is 0.13. If a customer shopped at Walbart in a given week, the probability that the customer returns to Walbart next week is 0.75 and the probability that the customer goes to H.E.D. the next week is 0.25. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at H.E.D. and a 0.5 probability that the customer shopped at Walbart at period 0; that is, a1(0) = 0.5 and T2(0) = 0.5. Given these initial state probabilities, answer the following questions (round to three decimal places): a. The probability that the consumer shops at H.E.D. in Period 2 = b. The probability that the consumer shops at Walbart in Period 6 = c. What is the long-run probability (or market share) of H.E.D? d. What is the long-run probability (or market share of Walbart?
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