1. This is a simulation question. Consider the Markov chain with the transition probability matrix 0.4 0.38 0.22 P = 0.12 0.7 0.13 0.2 0.5 0.3 a. Simulate and plot a single realization X0, . .. ,X... of this rnarkov chain (start it with X0 = 1). The plot should have time as the X-axis (going from I] to n) and the yaxis should have 1,2,3. In each point in time the Markov chain will be in one of the states. Use the time horizon in. = 100. b. Increase n to a 1000 and. Generate a single realizatiorr compute, over this realization 1 \"1 - E X 1.. n' k=0 and, for ,8 = 0.9 n E 3&1}? k32- k=0 As before, use X0 = 1 for your initial condition