2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doors out of the room. 2 1 3 4 + 5 6 (a) Write down the transition matrix for this Markov chain. [2] (b) What are the communicating classes for this Markov chain? Are they periodic? Justify your answer. [2] (c) Find the stationary distribution for this Markov chain. Demonstrate that it is the stationary distribution (i.e. do not simply write down a 7 with no justification) [3]
2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doors out of the room. 2 1 3 4 + 5 6 (a) Write down the transition matrix for this Markov chain. [2] (b) What are the communicating classes for this Markov chain? Are they periodic? Justify your answer. [2] (c) Find the stationary distribution for this Markov chain. Demonstrate that it is the stationary distribution (i.e. do not simply write down a 7 with no justification) [3]
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ:
12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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![2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random
one of the doors out of the room.
2
1
3
4
+
5
6
(a) Write down the transition matrix for this Markov chain. [2]
(b) What are the communicating classes for this Markov chain? Are they periodic? Justify your answer. [2]
(c) Find the stationary distribution for this Markov chain. Demonstrate that it is the stationary distribution
(i.e. do not simply write down a 7 with no justification) [3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc05cf68-81ae-4970-8864-261fc4d70f9c%2F9a992c93-e50e-4f72-93d8-8a9288ec7f20%2Fxo5hj2m_processed.png&w=3840&q=75)
Transcribed Image Text:2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random
one of the doors out of the room.
2
1
3
4
+
5
6
(a) Write down the transition matrix for this Markov chain. [2]
(b) What are the communicating classes for this Markov chain? Are they periodic? Justify your answer. [2]
(c) Find the stationary distribution for this Markov chain. Demonstrate that it is the stationary distribution
(i.e. do not simply write down a 7 with no justification) [3]
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