Consider the Markovj chain Xn with state space {0, 2} and with one-step transition probability matrix Px = 1/2 1/2 1/2 1/2 and the Markov chain Yn with state space {3, 4} and with one-step transition...

Consider the Markovj chain Xn with state space {0, 2} and with one-step transition probability matrix
Px =
1/2 1/2 1/2 1/2 and the Markov chain Yn with state space {3, 4} and with one-step transition probability matrix
Assume further that Xn and Yn are independent, for all it. Define Zn = Xn Yn. 1. What is the state space of Zn? Is Zn a Markov chain? Explain (a proof is not required). 2. Calculate the matrix Pz of the Markov chain Zn.