Question

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 the figure. 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 Pu1 = 0, P12- and P13 - 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. (from) Room 1 Room 2 Room 3 (to) Room 1 P. Room 2 0 Room 3 Predict the long-term distribution of rats. What is the long-term probability that a given marked rat is in room 1? eBook

Answer 1

Steady state vector, x satisfies Px=x. 710 2/3 12, ( 243 o 12 ) 1/3 43 • , . → 2X2 + { *3 = x, : 2 3x2-3x1 = x, _X2 3x + {X3 = x2 3x2 = 5x, 3x1 = x2 E5, + & X2 = X3 = 2* *x=1

* x= 3x G): I***** - H1+23 =83 MIDO 1 3/8) answer. Long-teom probability that a given rat is in room I = 3/8 answer