(a) Agency banking is a growing trend in the country. In an effort to improve customer service a monthly research on the switching patterns of clients from three Bank Agents A, B and C was conducted and recorded as shown below. Number of Clients. Banks Market Share. Gains from 30.4.2020 A B 0.294 400 120 0.471 300 140 0.235 100 510 A B 4000 8000 6000 1 0 Determine the transition matrix of the market controlled by the three Agents. Comment on your results. (3 Marks) (ii) Determine the market share percentage and number of clients visiting each of the three agents at the end of June 2020. Comment on your results. (4 Marks) (iii) Using appropriate calculations, advise on the nature of business in the long-run. Comment on your results. (4 Marks) (b) A Markov chain with three states has the following transition matrix 11-P 1-P 0 P 0 P 1-pp Determine the value of pif the long run probability of being in state three is 0.552. in da la (a) Agency banking is a growing trend in the country. In an effort to improve customer service a monthly research on the switching patterns of clients from three Bank Agents A, B and C was conducted and recorded as shown below. Number of Clients. Banks Market Share. Gains from 30.4.2020 A B 0.294 400 120 0.471 300 140 0.235 100 510 A B 4000 8000 6000 1 0 Determine the transition matrix of the market controlled by the three Agents. Comment on your results. (3 Marks) (ii) Determine the market share percentage and number of clients visiting each of the three agents at the end of June 2020. Comment on your results. (4 Marks) (iii) Using appropriate calculations, advise on the nature of business in the long-run. Comment on your results. (4 Marks) (b) A Markov chain with three states has the following transition matrix 11-P 1-P 0 P 0 P 1-pp Determine the value of pif the long run probability of being in state three is 0.552. in da la