Sequence of continuity

2. (15 pts) Consider a Markov chain { Xn } with state space S = {0, 1, 2} and transition matrix and transition matrix P = O ON/H HN/H O (1) Let the mapping f : S - S satisfy f(0) = 0 and f(2) = 1 and assume that f(1) # f(2). If Yn = f(Xn), then when is { Yn } a Markov chain? Is {Yn } always a Markov chain? In other words, are functions of Markov chains always Markov chains?Let {Xiji=1 36 be the sequence of continuous IIDRV with EXi = 40, Var Xi = 144, i = 1, ..., 36 and A36 Eil Xi = 36 (a) By using the Markov's inequality estimate P( A36