Homework Help is Here – Start Your Trial Now!
Math
Statistics
Problem 1: Consider a continuous Markov chain with two states S = {0,1}. Assume the holding time parameters are given by A> 0. That is, vo = v1 = d, that is, the time that the chain spends in each state before going to the other state has an Exponential(A) distribution. %3D 1. Draw the state diagram of the chain with the transition rates. Find Q.

Problem 1: Consider a continuous Markov chain with two states S = {0,1}. Assume the holding time parameters are given by A> 0. That is, vo = v1 = d, that is, the time that the chain spends in each state before going to the other state has an Exponential(A) distribution. %3D 1. Draw the state diagram of the chain with the transition rates. Find Q.

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

Do this question please ? i give pit upvote definitely 

Problem 1: Consider a continuous Markov chain with two states S = {0,1}. Assume the holding time parameters are given by A > 0. That is, vo = v1 = X, that is, the time that the chain spends in each state before going to the other state has an Exponential(A) distribution. 1. Draw the state diagram of the chain with the transition rates. Find Q. 2. Find the eigenvalues and eigenvectors of the matrix Q and use them to decompose Q = EDE-1, where D is the diagonal matrix with eigenvalues in the diagonal; (in decreasing order), and E is the matrix with the corresponding eigenvectors as columns. 3. Use the above to find the transition matrix P(t) = etQ = E2*DE-1. Pay attention to how the matrix elD was defined in class. Do the matrix multiplication to get the final answer. Take limit as t → o to find the steady state.
Transcribed Image Text:Problem 1: Consider a continuous Markov chain with two states S = {0,1}. Assume the holding time parameters are given by A > 0. That is, vo = v1 = X, that is, the time that the chain spends in each state before going to the other state has an Exponential(A) distribution. 1. Draw the state diagram of the chain with the transition rates. Find Q. 2. Find the eigenvalues and eigenvectors of the matrix Q and use them to decompose Q = EDE-1, where D is the diagonal matrix with eigenvalues in the diagonal; (in decreasing order), and E is the matrix with the corresponding eigenvectors as columns. 3. Use the above to find the transition matrix P(t) = etQ = E2*DE-1. Pay attention to how the matrix elD was defined in class. Do the matrix multiplication to get the final answer. Take limit as t → o to find the steady state.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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