A psychologist conducts an experiment in which 20 rats are placed at random in a

Chapter 3, Problem 5

(choose chapter or problem)

A psychologist conducts an experiment in which 20 rats are placed at random in a compartment that has been divided into rooms labeled 1, 2, and 3, as shown in Figure 3.2. 1 3 2 Figure 3.2 Observe that there are four doors in the arrangement. There are three possible states for the rats: they can be in room 1, 2, or 3. Let us assume that the rats move from room to room. A rat in room 1 has the probabilities p11 = 0, p12 = .and p13 = t of moving to the various rooms, based on the distribution of doors. This approach leads to a Markov chain with the following transition matrix P. Predict the long-term distribution of rats. What is the long-term probability that a given marked rat is in room 2? (from) Room 1 Room 2 Room 3 (to) p [l 2 !l Rooml 3 0 Room2 1 Room3