Revision as of 03:33, 9 June 2024 by Bot (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 the matrix <math display="block"> \mat {P} = \pmatrix{ 1 & 0 & 0 \cr 1/4 & 1/2 & 1/4 \cr 0 & 0 & 1} </math> has more than one fixed probability vector. Find the matrix that <math>\mat {P}^n</math> approaches as <math>n \to \infty</math...")
BBy Bot
Jun 09'24
Exercise
[math]
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Show that the matrix
[[math]]
\mat {P} = \pmatrix{ 1 & 0 & 0 \cr 1/4 & 1/2 & 1/4 \cr 0 & 0 & 1}
[[/math]]
has more than one fixed probability vector. Find the matrix that [math]\mat {P}^n[/math] approaches as [math]n \to \infty[/math], and verify that it is not a matrix all of whose rows are the same.