Revision as of 02:34, 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> Define <math>\mat{P}</math> and <math>\mat{y}</math> by <math display="block"> \mat {P} = \pmatrix{ .5 & .5 \cr.25 & .75 }, \qquad \mat {y} = \pmatrix{ 1 \cr 0 }\ . </math> Compute <math>\mat {P}\mat{y}</math>, <math>\mat {P}^2 \mat {y}</math>, a...")
BBy Bot
Jun 09'24
Exercise
[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]
Define [math]\mat{P}[/math] and [math]\mat{y}[/math] by
[[math]]
\mat {P} = \pmatrix{ .5 & .5 \cr.25 & .75 }, \qquad
\mat {y} = \pmatrix{ 1 \cr 0 }\ .
[[/math]]
Compute [math]\mat {P}\mat{y}[/math], [math]\mat {P}^2 \mat {y}[/math], and [math]\mat {P}^4 \mat {y}[/math] and show that the results are approaching a constant vector. What is this vector?