A fair die is tossed repeatedly. The maximum of the first n outcomes is denoted by X n . Is {X n : n = 1, 2,...} a Markov chain? Why or why not? If it is a Markov chain, calculate its transition...

A fair die is tossed repeatedly. The maximum of the first n outcomes is denoted by X_n. Is {X_n
: n = 1, 2,...} a Markov chain? Why or why not? If it is a Markov chain, calculate its transition probability matrix, specify the classes, and determine which classes are recurrent and which are transient.