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- 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)Consider a continuous time Markov chain with three states {0, 1, 2} and transitions rates as follows: q01 = 3, q12 = 5, q21 = 6, q10 = 4 and the remaining rates are zeros. Find the limiting probabilities for the chain.Consider the following stochastic system. Let Xn be the price of a certain stock (rounded to the nearest cent) at the time that the stock market closes on the n-th day starting today. Would it be appropriate to model this system as a Discrete-time Markov Chain?