3. Consider a Markov chain (Xn)n=0,1,2,... with state space S probability matrix = {1, 2, 3} and transition P = ( 1/5 3/5 1/5\ 0 1/2 1/2 3/10 7/10 0 The initial distribution is given by a = (1/2, 1/6, 1/3). Compute (a) P[X2 = k] for all k = 1, 2, 3; (b) E[X2]. Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the expected value of X2 computed in (b) depend on the initial distribution a? Give a reason for both of your answers.
3. Consider a Markov chain (Xn)n=0,1,2,... with state space S probability matrix = {1, 2, 3} and transition P = ( 1/5 3/5 1/5\ 0 1/2 1/2 3/10 7/10 0 The initial distribution is given by a = (1/2, 1/6, 1/3). Compute (a) P[X2 = k] for all k = 1, 2, 3; (b) E[X2]. Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the expected value of X2 computed in (b) depend on the initial distribution a? Give a reason for both of your answers.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
please solve it on paper
![3.
Consider a Markov chain (Xn)n=0,1,2,... with state space S
probability matrix
=
{1, 2, 3} and transition
P
=
(
1/5 3/5 1/5\
0 1/2 1/2
3/10 7/10 0
The initial distribution is given by a
= (1/2, 1/6, 1/3). Compute
(a) P[X2 = k] for all k = 1, 2, 3;
(b) E[X2].
Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the
expected value of X2 computed in (b) depend on the initial distribution a? Give a reason for
both of your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe4f043a-40ec-446c-a7ff-f52648c59722%2F831d82b9-784a-4e0d-8602-301de15d7718%2Ffy1zibm_processed.png&w=3840&q=75)
Transcribed Image Text:3.
Consider a Markov chain (Xn)n=0,1,2,... with state space S
probability matrix
=
{1, 2, 3} and transition
P
=
(
1/5 3/5 1/5\
0 1/2 1/2
3/10 7/10 0
The initial distribution is given by a
= (1/2, 1/6, 1/3). Compute
(a) P[X2 = k] for all k = 1, 2, 3;
(b) E[X2].
Does the distribution of X2 computed in (a) depend on the initial distribution a? Does the
expected value of X2 computed in (b) depend on the initial distribution a? Give a reason for
both of your answers.
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