Question: We consider the Markov chain modelling someone visiting three locations at random and going from one location to another according to the transition matrix [1/4

We consider the Markov chain modelling someone visiting three locations at random and going from one location to another according to the transition matrix [1/4 1/4 1/47 P = 3/4 3/4 1/4 0 1/2 0 a a (a) If the walker has a 50% chance to start in location 1 and a 50% chance to start in location 3, what is the probability he is in location 3 after two steps? Show your work. (b) Find the steady state vector for this system. We consider the Markov chain modelling someone visiting three locations at random and going from one location to another according to the transition matrix [1/4 1/4 1/47 P = 3/4 3/4 1/4 0 1/2 0 a a (a) If the walker has a 50% chance to start in location 1 and a 50% chance to start in location 3, what is the probability he is in location 3 after two steps? Show your work. (b) Find the steady state vector for this system

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