In a certain community, currently, 10% of the people are H (high income), 60% are M (medium income), and 30% are L (low income). Studies show that for the children of H parents, 50% also become H, 40% become M, and 10% become L. Of the children of M parents, 40% become H, 30% become M, and 30% become L. Of the children of L parents, 30% become H, 50% become M, and 20% become L.
(a) Set up the 3 × 3 stochastic matrix that describes this situation.
(b) What percent of the children of the current generation will have high incomes?
(c) In the long run, what percentage of the population will have low incomes?