Problem 1. A fair dice with numbers 1 through 6 is thrown infinitely often, with the outcome of each throw independent of all the other throws. For nc N, set X := je {1, ...,6} for j the maximum of the numbers that appeared on the first n throws of the dice. Set Xo :=1. (a) (10p) Show that (X, )" is a Markov chain on E = {1,...,6} and determine its transition matrix. (b) (10p) Determine the absorption probability in state 6 for every r E E