In a psychology experiment, a rat is placed in the maze shown in the figure. In each minute of the
observation, the rat may stay in the room it is in, or move to by any of the exits to another room.
For all rooms the probability of remaining in the room is 40%, reflecting the fact that rats and mice are
neophobic. The probability of using any of the exits from a room is the same. Thus for Room 2, the
probability of staying is 40%, the probability of exiting to Room 1, Room 3 or Room 5 is 20% (equally likely)
but the probability of exiting to Room 4 and 6 is 0 because there is no exit to these rooms.
Draw up the transition probability matrix for the system.
A rat is placed in Room 1. Find the probabilities of the rat being in each of the rooms after:
a) 1 minute
b) 3 minutes
c) What is the long-term probability of the rat ending in each of the rooms?