exercise:0760f55365: 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> Prove that, if a 3-by-3 transition matrix has the property that its ''column'' sums are 1, then <math>(1/3, 1/3, 1/3)</math> is a fixed probability vector. State a similar result for <math>n</math>-by-<math>n</math> transition matrices. Interpr...") |
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\newcommand{\mathds}{\mathbb}</math></div> Prove that, if a 3-by-3 transition matrix has the | \newcommand{\mathds}{\mathbb}</math></div> Prove that, if a 3-by-3 transition matrix has the property that its ''column'' sums are 1, then <math>(1/3, 1/3, 1/3)</math> is a fixed probability vector. State a similar result for <math>n</math>-by-<math>n</math> transition matrices. Interpret these results for ergodic chains. | ||
property | |||
that its ''column'' sums are 1, then <math>(1/3, 1/3, 1/3)</math> is a fixed | |||
probability | |||
vector. State a similar result for <math>n</math>-by-<math>n</math> transition matrices. Interpret | |||
these results for ergodic chains. | |||
Latest revision as of 22:51, 17 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]
Prove that, if a 3-by-3 transition matrix has the property that its column sums are 1, then [math](1/3, 1/3, 1/3)[/math] is a fixed probability vector. State a similar result for [math]n[/math]-by-[math]n[/math] transition matrices. Interpret these results for ergodic chains.