**Markov Chain Example**Given the Markov Chain $(S, x_0, P)$ where $S = \{s_1, s_2, s_3\}$, $x_0 = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}$, and\[ P = \begin{bmatrix}0 & .3 & .2 \\1 & 0 & .4 \\0 & .7 & .4 \end{bmatrix} \]\[P^2 = \begin{bmatrix}.3 & .14 & .2 \\0 & .58 & .36 \\.7 & .28 & .44 \end{bmatrix} \]\[P^3 = \begin{bmatrix}.14 & .23 & .196 \\.58 & .252 & .376 \\.28 & .518 & .428 \end{bmatrix} \]\[P^4 = \begin{bmatrix}.23 & .1792 & .1984 \\.252 & .4372 & .3692 \\.518 & .3836 & .4344 \end{bmatrix} \]\[P^5 = \begin{bmatrix}.1792 & .20788 & .19704 \\.4372 & .33264 & .37218 \\.3836 & .45948 & .4308 \end{bmatrix} \]\[P^6 = \begin{bmatrix}.20788 & .191688 & .197808 \\.33264 & .391672 & .36936 \\.45948 & .41664 & .432832 \end{bmatrix} \]Compute the probability that the Markov Chain is in state $s_1$ at time 6.---**Interpretation of Matrices:**In this case, each matrix $P^n$ represents the state transition probabilities after $n$ steps.For example:- $P^2$ indicates the state probabilities after 2 steps.- $P^3$ indicates the state probabilities after 3 steps.- and so on...As $n$ increases, $P^n$ gives the probabilities of being in each state after $n$ transitions, starting

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Given the Markov Chain (S, ro, P) where S = {$1, 82, 83}, To , and [o 3 .21 Г.3 .14 P = |1 0 .4 p² = |0 .58 .36 P3 = |.58 .252 .376 .7 .28 .44 .2 [.14 .23 .196] 0 .7 .4 28 .518 .428 .23 .1792 .1984] 252 4372 3692 p5 [.1792 .20788 .19704] .4372 33264 37218 p6 [.20788 .191688 .197808] 33264 391672 36936

Given the Markov Chain (S, ro, P) where S = {$1, 82, 83}, To , and [o 3 .21 Г.3 .14 P = |1 0 .4 p² = |0 .58 .36 P3 = |.58 .252 .376 .7 .28 .44 .2 [.14 .23 .196] 0 .7 .4 28 .518 .428 .23 .1792 .1984] 252 4372 3692 p5 [.1792 .20788 .19704] .4372 33264 37218 p6 [.20788 .191688 .197808] 33264 391672 36936

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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