Suppose you roll independently a die (a small cube marked on each side with one to six spots) multiple times. Let Em be the outcome of the nth roll and let Sn 2 23:] Za- be the sum of the outcomes in the rst it rolls. In each of the following oases1 argue (a rigorous proof is not required here) whether X : {X : o 3 1} is a Markov chain or not: (a) X\" = Z' {b} X1: 2 Sn {c} X\" 2 Sn + S _1, with the lmderstanding that H = {l (Hint: you might want to draw some sample paths of the process X in each case in order to gain some insight.)