1. Problem 15.12 Trees in a forest are assumed to fall into four age groups: baby trees (0-10 years of age), young trees (11-20 years of age), middle-aged trees

(21-30 years of age), and old trees (older than 30 years of age). The length of one time period is 10 years. In each time period a certain percentage of trees in each age group dies. These percentages are 20%, 5%, 10%, and 25% for the four age groups. Lost trees are replaced by baby trees. Surviving trees enter the next age group, where old trees remain in the fourth age group. Suppose that the forest is newly planted with 10,000 trees. What is the age distribution of the forest after 50 years? What is the age distribution of the forest in the equilibrium situation?

398 Markov chains