exercise:2e4acd3b92: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Show that if <math>\mat P</math> is the transition matrix of a regular Markov chain, and <math>\mat W</math> is the matrix each of whose rows is the fixed probability vector corresponding to <math>\mat {P}</math>, then <math>\mat {P}\mat {W} = \ma...") |
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\newcommand{\secstoprocess}{\all} | \newcommand{\secstoprocess}{\all} | ||
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\newcommand{\mathds}{\mathbb}</math></div> Show that if <math>\mat P</math> is the transition matrix of a | \newcommand{\mathds}{\mathbb}</math></div> Show that if <math>\mat P</math> is the transition matrix of a regular Markov chain, and <math>\mat W</math> is the matrix each of whose rows is the fixed probability vector corresponding to <math>\mat {P}</math>, then <math>\mat {P}\mat {W} = \mat {W}</math>, and <math>\mat{W}^k = \mat {W}</math> for all positive integers <math>k</math>. | ||
regular Markov | |||
chain, and <math>\mat W</math> is the matrix each of whose rows is the fixed probability | |||
vector | |||
corresponding to <math>\mat {P}</math>, then <math>\mat {P}\mat {W} = \mat {W}</math>, and <math>\mat | |||
{W}^k = \mat {W}</math> | |||
for all positive integers <math>k</math>. | |||
Latest revision as of 02:32, 15 June 2024
[math]
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}[/math]
Show that if [math]\mat P[/math] is the transition matrix of a regular Markov chain, and [math]\mat W[/math] is the matrix each of whose rows is the fixed probability vector corresponding to [math]\mat {P}[/math], then [math]\mat {P}\mat {W} = \mat {W}[/math], and [math]\mat{W}^k = \mat {W}[/math] for all positive integers [math]k[/math].