State transition diagram

7. (Bonus) a. Sketch the state-transition diagram for the Markov chain with the following transition probability matrix: (1.5 points) 0.5 0.5 0 1.0 0 0 0 P = 0.5 0 0.25 0.25 0 0.25 0.25 0.5 b. Find the transition probability matrix for the Markov chain shown. (1.5 points) 0.5 3 0.56. A Markov chain with the states 1, 2, 3 has transition probability matrix: 1 . P: 2 0.4 0.3 b 3 (a) Give the values of a, b, and c that make the above a valid transition probability matrix. (3 points) Question 1: (a) A Markov chain {Xn} on the state space S = {0,1,2} has the transition probabilities matrix: 0.3 0.2 0.51 P = 0.2 0.7 0.1 0 0.4 0.6] Find (i) The two-steps transition probability matrix (3 marks) (ii) P[X2 = 2, X3 = 1/X1 = 0] (4 marks)Question 20 1 pts Let P be the transition matrix of a Markov chain with n states. Which one of the following statements is not always true? If Q is another transition matrix of a Markov chain with n states, then =(P + Q) is the transition matrix of a Markov chain with n states. O P2 is the transition matrix of a Markov chain with n states. If P is invertible, then p-1 is the transition matrix of a Markov chain with n states. If Q is another transition matrix of a Markov chain with n states, then PQ is the transition matrix of a Markov chain with n states.10. A 3-state Markov chain { Xn, n = 0, 1, ...} has the transition probability matrix 0.1 0.2 0.7 0.2 0.2 0.6 0.6 0.1 0.3 (a) Find the two-step transition probability matrix P2. (b) Calculate Pr{X3 = 1/X1 = 0}. (c) Calculate Pr{X3 =1/Xo = 0} using the Chapman-Kolmogorov equation