Question

(Markov Chain) The textbook contains a brief discussion of Markov Chains on pp.305–310. It may help you with the following problem.

In the Dark Ages, Harvard, Dartmouth, and Yale admitted only male students. Assume that, at that time, 80 percent of the sons of Harvard men went to Harvard and the rest went to Yale, 40 percent of the sons of Yale men went to Yale, and the rest split evenly between Harvard and Dartmouth; and of the sons of Dartmouth men, 70 percent went to Dartmouth, 20 percent to Harvard, and 10 percent to Yale. This information can be expressed by a matrix

M = 0.8 0.2 0

0.3 0.4 0.3

0.2 0.1 0.7
Use that matrix to find the probability that a grandson of a man from Harvard went to Harvard;

went to Yale; went to Dartmouth. Find the same for gran-grandson of a man from Yale.

Answer 1