Homework Help is Here – Start Your Trial Now!
Math
Statistics
1. (a) Consider a discrete-time Markov chain X = {X₂ : n = N} with a transition matrix 0 2/3 1/3 M = 1/3 0 2/3 1/4 3/4 0 (1) i. Draw the transition diagram of X. ii. Is the Markov chain irreducible and positive recurrent? Justify your arguments. iii. Determine the stationary distribution л of X from the equation лM = π. (b) Let X = {X: t≥ 0} be a time-homogeneous Markov process with state-space $ = {1, 2, 3}. The average time X spends in each state 1, 2 and 3 is given respectively by 1/6, 1/2 and 1/3 unit of time. The probability P(XT j|X₁ = i) of making an immediate jump from state i to state j, with (i, j) = S, is given by the matrix M (1) in the question 1(a) above. Note that T refers to the jump time of the Markov process. = i. Find the corresponding intensity matrix Q of the Markov process. ii. Find the average time it takes the process to move from states 1 and 2 to state 3.

1. (a) Consider a discrete-time Markov chain X = {X₂ : n = N} with a transition matrix 0 2/3 1/3 M = 1/3 0 2/3 1/4 3/4 0 (1) i. Draw the transition diagram of X. ii. Is the Markov chain irreducible and positive recurrent? Justify your arguments. iii. Determine the stationary distribution л of X from the equation лM = π. (b) Let X = {X: t≥ 0} be a time-homogeneous Markov process with state-space $ = {1, 2, 3}. The average time X spends in each state 1, 2 and 3 is given respectively by 1/6, 1/2 and 1/3 unit of time. The probability P(XT j|X₁ = i) of making an immediate jump from state i to state j, with (i, j) = S, is given by the matrix M (1) in the question 1(a) above. Note that T refers to the jump time of the Markov process. = i. Find the corresponding intensity matrix Q of the Markov process. ii. Find the average time it takes the process to move from states 1 and 2 to state 3.

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

i need this question done in 10 minutes 

1. (a) Consider a discrete-time Markov chain X = {X₂ : n = N} with a transition matrix 0 2/3 1/3 M = 1/3 0 2/3 1/4 3/4 0 (1) i. Draw the transition diagram of X. ii. Is the Markov chain irreducible and positive recurrent? Justify your arguments. iii. Determine the stationary distribution л of X from the equation лM = π. (b) Let X = {X: t≥ 0} be a time-homogeneous Markov process with state-space $ = {1, 2, 3}. The average time X spends in each state 1, 2 and 3 is given respectively by 1/6, 1/2 and 1/3 unit of time. The probability P(XT j|X₁ = i) of making an immediate jump from state i to state j, with (i, j) = S, is given by the matrix M (1) in the question 1(a) above. Note that T refers to the jump time of the Markov process. = i. Find the corresponding intensity matrix Q of the Markov process. ii. Find the average time it takes the process to move from states 1 and 2 to state 3.
Transcribed Image Text:1. (a) Consider a discrete-time Markov chain X = {X₂ : n = N} with a transition matrix 0 2/3 1/3 M = 1/3 0 2/3 1/4 3/4 0 (1) i. Draw the transition diagram of X. ii. Is the Markov chain irreducible and positive recurrent? Justify your arguments. iii. Determine the stationary distribution л of X from the equation лM = π. (b) Let X = {X: t≥ 0} be a time-homogeneous Markov process with state-space $ = {1, 2, 3}. The average time X spends in each state 1, 2 and 3 is given respectively by 1/6, 1/2 and 1/3 unit of time. The probability P(XT j|X₁ = i) of making an immediate jump from state i to state j, with (i, j) = S, is given by the matrix M (1) in the question 1(a) above. Note that T refers to the jump time of the Markov process. = i. Find the corresponding intensity matrix Q of the Markov process. ii. Find the average time it takes the process to move from states 1 and 2 to state 3.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 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