exercise:9265c9975a: 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> 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...") |
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\mat {P} = \pmatrix{ 1/2 & 1/3 & 1/6 \cr3/4 & 0 & 1/4 \cr 0 & 1 & 0}\ . | \mat {P} = \pmatrix{ 1/2 & 1/3 & 1/6 \cr3/4 & 0 & 1/4 \cr 0 & 1 & 0}\ . | ||
</math> | </math> | ||
<ul><li> Show that this is a regular Markov chain. | <ul style="list-style-type:lower-alpha"><li> Show that this is a regular Markov chain. | ||
</li> | </li> | ||
<li> The process is started in state 1; find the probability that it is in | <li> The process is started in state 1; find the probability that it is in | ||
Latest revision as of 21:45, 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]
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].