(2 points) A retailer stocks three brands of breakfast cereal. A survey is taken of 6000 people who purchase cereal weekly from this retailer. Each week Cereal X loses 20% of its customers to Cereal Y and 50% to Cereal 2. Also, Cereal Y loses 10% of its customers to Cereal X and 30% to Cereal 2. Finally, Cereal Z loses 50% of its customers to Cereal X and 10% to Cereal Y. (a) Set up a stochastic matrix displaying these transitions. Its rows/columns should refer to the cereals X, Y, Z in this order. (b) Suppose that this week's sales are equally divided between the three brands, with 2000 people buying each. How many people will buy Cereal Y next week? (c) Under the assumptions of (b), how many people will buy Cereal 2 in two weeks