Let Yn be the outcome of the nth toss of a six-sided die: Yn {1, 2, . . . , 6}. For n 1, let Sn = Y1+Y2+...+Yn and Xn = (Sn mod 7), i.e., Xn is the remainder when Sn is divided by 7. Show that {Xn, n 1} is a DTMC and display its transition probability matrix. Assume that successive tosses are independent.

Let Yn be the outcome of the nth toss of a six-sided die: Yn E {1, 2, ..., 6}. For n 2 1, let Sn = YitY2+... + Yn and Xn = (Sn mod 7), i.e., Xn is the remainder when Sn is divided by 7. Show that {Xn, n 2 1} is a DTMC and display its transition probability matrix. Assume that successive tosses are independent