Consider the Markov chain on {1, 2, 3} with transition matrix P = [ 1 / 2 0 1 / 2 1 / 2 1 / 2 0 0 1 / 2 1 / 2 ] a. Show that P is a regular matrix. b. Find the steady-state vector for this Markov chain. c. What fraction of the time does this chain spend in state 2? Explain your answer.
Consider the Markov chain on {1, 2, 3} with transition matrix P = [ 1 / 2 0 1 / 2 1 / 2 1 / 2 0 0 1 / 2 1 / 2 ] a. Show that P is a regular matrix. b. Find the steady-state vector for this Markov chain. c. What fraction of the time does this chain spend in state 2? Explain your answer.
Solution Summary: The author explains that a stochastic matrix P is regular if some power Pk contains only positive entries.
Consider the Markov chain on {1, 2, 3} with transition matrix
P =
[
1
/
2
0
1
/
2
1
/
2
1
/
2
0
0
1
/
2
1
/
2
]
a. Show that P is a regular matrix.
b. Find the steady-state vector for this Markov chain.
c. What fraction of the time does this chain spend in state 2? Explain your answer.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY