Question 2[10 marks ] A fair die is rolled repeatedly. Determine which of the following are Markov chains, and for those that are, provide their state spaces and one-step transition matrices. Here n=0,1,2,. (a) (2 points) The largest number Mn in the first n rolls. (b) ( 2 points) The number Nn of sixes in the first n rolls. (c) (2 points) After the nth roll, the (nonnegative) number An of rolls since the last six (with An:=n if no sixes have appeared). (d) (2 points) After the nth roll, the (positive) number Bn of rolls until the next six. (e) (2 points) Cn:=An+Bn. Question 2[10 marks ] A fair die is rolled repeatedly. Determine which of the following are Markov chains, and for those that are, provide their state spaces and one-step transition matrices. Here n=0,1,2,. (a) (2 points) The largest number Mn in the first n rolls. (b) ( 2 points) The number Nn of sixes in the first n rolls. (c) (2 points) After the nth roll, the (nonnegative) number An of rolls since the last six (with An:=n if no sixes have appeared). (d) (2 points) After the nth roll, the (positive) number Bn of rolls until the next six. (e) (2 points) Cn:=An+Bn