exercise:83d666c19f: 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> A certain experiment is believed to be described by a two-state Markov chain with the transition matrix <math>\mat{P}</math>, where <math display="block"> \mat {P} = \pmatrix{ .5 & .5 \cr p & 1 - p} </math> and the parameter <math>p</math> is no...") |
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\newcommand{\secstoprocess}{\all} | \newcommand{\secstoprocess}{\all} | ||
\newcommand{\NA}{{\rm NA}} | \newcommand{\NA}{{\rm NA}} | ||
\newcommand{\mathds}{\mathbb}</math></div> A certain experiment is believed to be described by a | \newcommand{\mathds}{\mathbb}</math></div> A certain experiment is believed to be described by a two-state Markov chain with the transition matrix <math>\mat{P}</math>, where | ||
two-state Markov chain with the transition matrix <math>\mat{P}</math>, where | |||
<math display="block"> | <math display="block"> | ||
\mat {P} = \pmatrix{ .5 & .5 \cr p & 1 - p} | \mat {P} = \pmatrix{ .5 & .5 \cr p & 1 - p} | ||
</math> | </math> | ||
and the parameter <math>p</math> is not known. When the experiment is performed many | |||
times, the chain ends in state one approximately 20 percent of the time and in | and the parameter <math>p</math> is not known. When the experiment is performed many times, the chain ends in state one approximately 20 percent of the time and in state two approximately 80 percent of the time. Compute a sensible estimate for the unknown parameter <math>p</math> and explain how you found it. | ||
state two approximately 80 percent of the time. Compute a sensible estimate | |||
for the unknown parameter <math>p</math> and explain how you found it. | |||
Latest revision as of 22:02, 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]
A certain experiment is believed to be described by a two-state Markov chain with the transition matrix [math]\mat{P}[/math], where
[[math]]
\mat {P} = \pmatrix{ .5 & .5 \cr p & 1 - p}
[[/math]]
and the parameter [math]p[/math] is not known. When the experiment is performed many times, the chain ends in state one approximately 20 percent of the time and in state two approximately 80 percent of the time. Compute a sensible estimate for the unknown parameter [math]p[/math] and explain how you found it.