In the market share analysis of Section 17.1, 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 Murphy€™s and a 0.5 probability that the customer shopped at Ashley€™s at period 0; that is, Ï€1(0) = 0.5 and Ï€2(0) = 0.5. Given these initial state probabilities, develop a table similar to Table, showing the probability of each state in future periods. What do you observe about the long-run probabilities of each state?

TABLE
STATE PROBABILITIES FOR FUTURE PERIODS BEGINNING INITIALLY
WITH A MURPHY€™SCUSTOMER

Transcribed Image Text:

Period (n) State Probability 3 10 꺼(n) 1 0.9 0.83 0.781 0.747 0.723 0.706 0.694 0.686 0.680 0.676 꺼(n) 0 0.1 0.17 0.219 0.253 0.277 0.294 0.306 0.314 0.320 0.324