Chapter 8.1, Problem 26E

Analysis of a Poem In 1913, Markov analyzed a long poem written by a Russian author. He found that vowels were followed by consonants 87.2% of the time (either in the same word or the next word) and that consonants were followed by vowels 66.3% of the time. (Source: Bulletin de l’Académie Imperiale des Sciences de St Petersburg. Published by l’Académie.démie.)

a. Set up the $2\times 2$ stochastic matrix, with columns and rows labeled V and C that describes this situation.

b. Find the probability that the second letter following a vowel is also a vowel.