Each morning, an individual leaves his house and goes on a run. He is equally likely to leave from the front door or back door. Upon leaving the house, he chooses a pair of running shoes (or goes barefoot if there are no shoes near the door from which the runner departs). Upon his return, independently of the door from which he left, he is equally likely to enter the house through either door. He leaves his shoes near the door through which he enters. Suppose that the runner owns 4 pairs of running shoes. Let Xn be the number of pairs of shoes at the front door each morning before he goes on the run. Then_____is a Markov chain.

Markov chain is a mathematical technique which is used to identify the transitions from one state to another according to probabilistic rules. This enables us to identify how certain object will reach at its future state. In the given scenario there are four pairs of shoes available to an individual. The runner can choose the pair of shoes based on which door he selects to go out. Markov chain technique will be used to identify the pairs of shoes that will be selected by the runner.