exercise:93a3662cf8: 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> Which of the following matrices are transition matrices for regular Markov chains? <ul><li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr .5 & .5 }</math>. \smallskip </li> <li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr 1 & 0 }</math>. \smallskip </li> <li...") |
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\newcommand{\mathds}{\mathbb}</math></div> Which of the following matrices are transition matrices | \newcommand{\mathds}{\mathbb}</math></div> Which of the following matrices are transition matrices for regular Markov chains? | ||
for | <ul style="list-style-type:lower-alpha"><li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr .5 & .5 }</math> | ||
regular Markov chains? | |||
<ul><li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr .5 & .5 }</math> | |||
</li> | </li> | ||
<li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr 1 & 0 }</math> | <li> <math>\mat {P} = \pmatrix{ .5 & .5 \cr 1 & 0 }</math> | ||
</li> | </li> | ||
<li> <math>\mat {P} = \pmatrix{ 1/3 & 0 & 2/3 \cr 0 & 1 & 0 \cr 0 & 1/5 & 4/5}</math> | <li> <math>\mat {P} = \pmatrix{ 1/3 & 0 & 2/3 \cr 0 & 1 & 0 \cr 0 & 1/5 & 4/5}</math> | ||
</li> | </li> | ||
<li> <math>\mat {P} = \pmatrix{ 0 & 1 \cr 1 & 0}</math> | <li> <math>\mat {P} = \pmatrix{ 0 & 1 \cr 1 & 0}</math> | ||
</li> | </li> | ||
<li> <math>\mat {P} = \pmatrix{ 1/2 & 1/2 & 0 \cr 0 & 1/2 & 1/2 \cr 1/3 & 1/3 & | <li> <math>\mat {P} = \pmatrix{ 1/2 & 1/2 & 0 \cr 0 & 1/2 & 1/2 \cr 1/3 & 1/3 & | ||
1/3}</math> | 1/3}</math> | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 21:45, 17 June 2024
[math]
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Which of the following matrices are transition matrices for regular Markov chains?
- [math]\mat {P} = \pmatrix{ .5 & .5 \cr .5 & .5 }[/math]
- [math]\mat {P} = \pmatrix{ .5 & .5 \cr 1 & 0 }[/math]
- [math]\mat {P} = \pmatrix{ 1/3 & 0 & 2/3 \cr 0 & 1 & 0 \cr 0 & 1/5 & 4/5}[/math]
- [math]\mat {P} = \pmatrix{ 0 & 1 \cr 1 & 0}[/math]
- [math]\mat {P} = \pmatrix{ 1/2 & 1/2 & 0 \cr 0 & 1/2 & 1/2 \cr 1/3 & 1/3 & 1/3}[/math]