Consider a Markov chain {Xn n = 0,1,...} with state space S : probability to start in one of these states. = {1, 2, 3, 4, 5} and an equal 2.1 Find an expression for P(X = 2, X = 1, X2 = 5, X3 = 2) in terms of transition probabilities. What important result does this example illustrate? (2) For the following questions, use the transition probability matrix: 1 0 0 0 1 0 0 0 0 P = 00 1 0 0 0 0 0.5 0.5 0 10 0 00 2.2 Draw the transition diagram. Find the classes and classify the states of this chain. 2.3 Find P(X5 = 3|X2 = 4). 2.4 Find P(X0=5|X2 = 2). (4) (2) (3)