Example 11.6 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. We form a Markov chain with transition matrix
Page 414 #4 For Example 11.6, find the probability that the grandson of a man from Harvard went to Harvard.
college_rates <- matrix(c(0.8,0.2,0,0.3,0.4,0.3,0.2,0.1,0.7),byrow=T,nrow=3)
P2 <- college_rates %*% college_rates
P2[1,1]## [1] 0.7Harvard_grandson = (0.8*0.8 + 0.2*0.3 + 0.2*0)
Harvard_grandson## [1] 0.7