Let P be the one-step transition probability matrix of a Markov chain that takes value from {0, 1, 2, 3, 4}. We have P = - 11 2011 0 2 0 0 0 1 0 o P3 1,4 。 P0,1 0 x 0 o limn→∞ PA 1,4 o limn→ 4 0 a. Specify the classes of the Markov chain. Classify each state i € {0, 1, 2, 3, 4} into either transient or recurrent state. 0 b. Let f; be the probability that starting at state i, the Markov chain will ever reenter state i. Calculate fi for all i = {0, 1, 2, 3, 4}. P₂ 4,3 4 c. Denote Pm as the (i, j)th entry of Pm where i, je {0, 1, 2, 3, 4}. Is each of the following quantities non-zero? Briefly explain why. 1 0 1 13
Let P be the one-step transition probability matrix of a Markov chain that takes value from {0, 1, 2, 3, 4}. We have P = - 11 2011 0 2 0 0 0 1 0 o P3 1,4 。 P0,1 0 x 0 o limn→∞ PA 1,4 o limn→ 4 0 a. Specify the classes of the Markov chain. Classify each state i € {0, 1, 2, 3, 4} into either transient or recurrent state. 0 b. Let f; be the probability that starting at state i, the Markov chain will ever reenter state i. Calculate fi for all i = {0, 1, 2, 3, 4}. P₂ 4,3 4 c. Denote Pm as the (i, j)th entry of Pm where i, je {0, 1, 2, 3, 4}. Is each of the following quantities non-zero? Briefly explain why. 1 0 1 13
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Let P be the one-step transition probability matrix of a
Markov chain that takes value from {0, 1, 2, 3, 4}. We
have
P=
=
LBLOO
0
0
o P3
1,4
230
1
20 O
0 0
1
4
0
o p5
0,1
o limn→∞ P1,4
o limn→∞ P 4,3
140
1
1
1
0/0/3/3/3
a. Specify the classes of the Markov chain. Classify
each state į € {0, 1, 2, 3, 4} into either
transient or recurrent state.
b. Let ƒ; be the probability that starting at state i,
the Markov chain will ever reenter state i.
Calculate fi for all i = {0, 1, 2, 3, 4).
c. Denote P as the (i, j)th entry of Pm where
i, je {0, 1, 2, 3, 4}. Is each of the following
quantities non-zero? Briefly explain why.
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