10: Consider the Markov chain on states 1,2,3,4, 5,6 with transition matrix LMOODO \"010000 gag-.0000 CCOl'HH 0059000 (3050:2303 This has period 3. (a) What are the periodic groupings? That is. states that are accessible to each other in exactly 3 steps form each group. (b) For each grouping, write down the 3 step transition matrix for states withing the group (all other entries of P3 are 0). (c) The stationary and limiting distributions in (b) can be trivially determined. What are they? Write down what I33\"3 and 133'\" and P3\"? converge to for large powers of t and the stationary distribution for the original chain