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)

a) Is {X_n} n>=0 a Markov Chain? Why or why not?

b) Find the transition probability matrix for {X_n}

c) Let T = min{n>=1:X_n>=4}, and suppose lambda = 3. Find E(T)