1.* A particle moves on a circle through points that have been marked 0, 1, 2, 3, 4 (in a clockwise.


1.* A jot moves on a divergence through summits that accept been conspicuous 0, 1, 2, 3, 4 (in a clockwise order). The jot starts at summit 0. At each tread it has appearance 0.5 of moving one summit clockwise (0 follows 4) and 0.5 of moving one summit counterclockwise. Let Xn (n _ 0) denote its dregs on the divergence behind tread n. {Xn} is a Markov security. (a) Construct the (one-step) transition matrix. (b) Use your OR Courseware to bisecticularize the n-tread transition matrix P(n) for n _ 5, 10, 20, 40, 80. (c) Use your OR Courseware to bisecticularize the steady-declare probabilities of the declare of the Markov security. Describe how the probabilities in the n-step transition matrices obtained in bisect (b) compare to these steady-declare probabilities as n grows large.