3.) A container holds three coupons, one red. one blue and one green. At each time n : 1.2. . .. one coupon is drawn from the container. its color observed and then it is replaced. Assume draws are independent over time and each time it is equally likely to draw each color. Let {Xni denote the number of distinct coupons seen up to time n with X0 : 0 (eg.} if only the red and blue coupons have been seen after 5 draws, then X5 : 2). a) Briey explain why {Xn} is a Markov chain. b) Draw and clearly label the transition diagram of this Markov chain. c) What is the expected number of draws needed until all coupons have been seen at least once