Markov Analysis 1 Two supermarkets serving the Northside area of San Antonio, HED and Walbart, are i

Markov Analysis 1 Two supermarkets serving the Northside area of San Antonio, HED and Walbart, are i

Markov Analysis

1 Two supermarkets serving the Northside area of San Antonio, HED 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 HED in a given week, the probability that the customer returns to HED next week is 09 and the probability that the customer goes to Walbart is 01 If a customer shopped at Walbart in a given week, the probability that the customer returns to Walbart next week is 08 and the probability that the customer goes to HED the next week is 02 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 05 probability that the customer shopped at HED and a 05 probability that the customer shopped at Walbart at period 0; that is, ?1(0) = 05 and ?2(0) = 05 Given these initial state probabilities, develop a table similar showing the probability of each state in future periods What do you observe about the long-run probabilities of each state?

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