Problem 5 A random walker walks among 3 points labelled {a, b, c}. Each minute, she takes a step, and her movement dynamics are as follows: If (current position) equals (previous-minute position), then go to any one of the other two positions with equal probability; If (current position) does not equal (previous-minute position), then continue to stay in current position during the next minute. (a)Determine the state-space, such that the system evolution can be described by a Discrete Time Markov Chain. Justify your answer. Draw the state transition diagram, with the states labeled and the edges labeled with the transition probabilities. (b)Consider the Markov chain in this problem. Is the Markov chain irreducible and aperiodic?