Question

Each morning Jeff leaves his house and goes for a run (to the pub. He is equally likely to leave either from his front or back door. Upon leaving his house, he chooses a pair of running shoes (or goes running barefoot if there are no shoes at the door from which he departed) On his return he is equally likely to enter, and leave his running shoes, either by the front door or back door. Assume he has 2 pairs of running shoes and let Xn be the number of pairs of running shoes at the front door before he goes for a run in the morning of the nth day, what is the state space of this process? Argue briefly that {X n20 is a Markov chain and determine ts transition matrix.

Answer 1