A mouse is put into the maze shown below. In each time period it randomly chooses a door of the compartment it is in and moves into another compartment.
a) Letting the compartment numbers represent the states of a markov chain, write the transition matrix.
b) Determine the long run fraction of time the mouse will spend in each compartment.
c) Make compartments 3 and 4 into absorbing states by assuming that the mouse must stay in those compartments once entered and write the new transition matrix.
d) In part c) what is the average number of steps it will take a mouse who begins in state 1 to be absorbed?
e) In part c) what is the probability that a mouse that begins in state 1 will be absorbed in compartment 3?
