Suppose that Y'n are i.i.d. random variables such that P(Yn = 0) = , P(Yn = 1) = =, P(Yn = 2) = N We define Xo = 3, and Xn for n 2 1 as follows If Yn = 0, then Xn = max{Xn-1 - 1,1} If Y > 0, then X, = min {Xn-1+ Ym, 3} Is the sequence X, is a Markov process? Explain. Find the transition matrix P C) Find the stationary distribution.2} Central Limit Theorem A casino opens in town. To attract customers, the owner offers the following deal on Roulette: (The deal is only open to the rst 2500 bets) Any person who bets $10 on red gets halftheir money back if they lose their bet, while they get the payout of $20 if they win the best { A bet on red is lost with probability 101'3? and is won with probability 13l3?.] Use the normal distribution to approximate the probability that the owner will lose more than $6500 on the promotional offer