Q6 thank you

persons in the population at the end of the nth period. Specify the transition probability matrix, justify your answer. 6. (Problem 3.1.4 in Pinsky and Karlin) The random variables {1,52, . .. are independent and with the common probability mass function Pr( = 0) = 0.2,Pr( = 1) = 0.3, P'r( = 2) = 0.3 and P115 = 3) = 0.2. Set X0 = 0, and let X7; = max{1, . . . ,En} be the largest 5 observed to date. Determine the transition probability matrix for the Markov chain {X71}, justify your answer. 7. (Problem 3.2.1 in Pinsky and Karlin) Consider the Markov chain whose transition probability matrix is given