It is the third task in the Triwizard Tournament and Harry Potter has been given a map of the magic maze which has been separated into 6 sections. Once leaving a section, the maze will send Harry along a path indicated by the arrows pictured below (the double arrows imply that the states at each end are accessible from each other in one step). When leaving a section, the maze is equally likely to send Harry down cach potential path. Assume we are interested in recording the section that Harry is in each time he moves.

(a) Develop a DTMC model that can be used to model Harry's movements throughout the maze. Be sure to define a state space and the one-step state transition probability matrix, P. Is the DTMC ergodic? Why or why not? (8)