## Question

# A psychologist conducts an experiment on rats. She puts a rat in a cage having three rooms labeled 1, 2, and 3, as shown

## A psychologist conducts an experiment on rats. She puts a rat in a cage having three rooms labeled 1, 2, and 3, as shown in Figure below. L Figure: a cage with 3 rooms and 5 doors. The rats are trained to select a door at random and move from one room to another when a bell is rung. a). (4 points) Build the transition matrix, T, of the Markov chain model. b). (8 points) If a rat is initially in room 3, what is the probability that this rat will be in room 2 after the bell has rung five times? (Use MATLAB/Python if necessary) c). (8 points) What is the long-term behavior of this Markov chain? Determine the steady-state vector and interpret it. (Use MATLAB/Python if necessary).

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