Homework Help is Here – Start Your Trial Now!
Math
Statistics
In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1. a) Show that a Markov chain with transition matrix 0 0 1/4 1/2 1/4 00 1 P has more than one stationary distributions. b) Using R and the code provided on find the matrix that Pn converges to, as n→∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.

In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1. a) Show that a Markov chain with transition matrix 0 0 1/4 1/2 1/4 00 1 P has more than one stationary distributions. b) Using R and the code provided on find the matrix that Pn converges to, as n→∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Show full answers and steps to this exercise using the Markov Chain Model Theorem 3
[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1. a) Show that a Markov chain with transition matrix 1 0 0 P= 1/4 1/2 1/4 0 1 [/ 0 has more than one stationary distributions. b) Using R and the code provided on find the matrix that P" converges to, as n→ ∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.
Transcribed Image Text:[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1. a) Show that a Markov chain with transition matrix 1 0 0 P= 1/4 1/2 1/4 0 1 [/ 0 has more than one stationary distributions. b) Using R and the code provided on find the matrix that P" converges to, as n→ ∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS