exercise:D92d290e31: 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> In Example, define <math>f(i)</math> to be the proportion of G genes in state <math>i</math>. Show that <math>f</math> is a harmonic function (see Exercise Exercise). Why does this sho...") |
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\newcommand{\mathds}{\mathbb}</math></div> In [[guide:52e01d4de7#exam 11.1.9 |Example]], define <math>f(i)</math> to be the | \newcommand{\mathds}{\mathbb}</math></div> In [[guide:52e01d4de7#exam 11.1.9 |Example]], define <math>f(i)</math> to be the proportion of G genes in state <math>i</math>. Show that <math>f</math> is a harmonic function (see [[exercise:Bc093aec03 |Exercise]]). Why does this show that the probability of being absorbed in state <math>(\mbox{GG},\mbox{GG})</math> is equal to the proportion of G genes in the starting state? (See [[exercise:Dcf7521d90 |Exercise]].) | ||
proportion of G genes in state <math>i</math>. Show that <math>f</math> is a harmonic function (see | |||
absorbed in state <math>(\mbox{GG},\mbox{GG})</math> is equal to the proportion of G genes | |||
in | |||
the starting state? (See | |||
Latest revision as of 01:44, 16 June 2024
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\newcommand{\mat}[1]{{\bf#1}}
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\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}[/math]
In Example, define [math]f(i)[/math] to be the proportion of G genes in state [math]i[/math]. Show that [math]f[/math] is a harmonic function (see Exercise). Why does this show that the probability of being absorbed in state [math](\mbox{GG},\mbox{GG})[/math] is equal to the proportion of G genes in the starting state? (See Exercise.)