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  
Exercise [[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 [[exercise:Dcf7521d90 |Exercise]].)

Latest revision as of 00:44, 16 June 2024

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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.)