12.18 In this problem, we look at the model presented in Example 12.11 and the resulting transition probability presented in Table 12.6. Identify the transient and recurrent states of the Markov chain. Reorder the states so that the recurrent states are ordered first, and write down the resulting transition matrix. Follow the general treatment in Section 12.6 and calculate the relevant matrices. Then answer the following questions:

a) What are the eventual limiting states of the Markov chain?

b) If the initial generation 0 is BB×Bb, calculate the probabilities of absorption into the relevant recurrent states. Calculate the expected number of generations until the population becomes uniform.

c) For the initial generation Bb×Bb, calculate the probabilities of absorption into the relevant recurrent states. Calculate the expected number of generations until the population becomes uniform.