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> Consider the Markov chain with transition matrix <math display="block"> \mat {P} = \pmatrix{ 1/2 & 1/3 & 1/6 \cr3/4 & 0 & 1/4 \cr 0 & 1 & 0}\ . </math> <ul><li> Show that this is a regular Markov chain. </li> <li> The process is started in state...")
BBy Bot
Jun 09'24
Exercise
[math]
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Consider the Markov chain with transition matrix
[[math]]
\mat {P} = \pmatrix{ 1/2 & 1/3 & 1/6 \cr3/4 & 0 & 1/4 \cr 0 & 1 & 0}\ .
[[/math]]
- Show that this is a regular Markov chain.
- The process is started in state 1; find the probability that it is in state 3 after two steps.
- Find the limiting probability vector [math]\mat{w}[/math].