Suppose Y_0, Y_1,.... is a sequence of independent and identically distributed Poisson random variables with mean lambda. Let:

p_i = P(Y_n = i), for i = 0, 1, 2,...

For n = 0, 1,....., let X_n = max(Y_0, y_1,......,Y_n)

Find the transition probability matrix for {X_n}