exercise:Dcf7521d90: 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> Show that in both Example and the example just given, the probability of absorption in a state having genes of a particular type is equal to the proportion of genes of that type in the starting state. Show that t...") |
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\newcommand{\mathds}{\mathbb}</math></div> Show that in both [[guide:52e01d4de7#exam 11.1.9 |Example]] and the | \newcommand{\mathds}{\mathbb}</math></div> Show that in both [[guide:52e01d4de7#exam 11.1.9 |Example]] and the example just given, the probability of absorption in a state having genes of a particular type is equal to the proportion of genes of that type in the starting state. Show that this can be explained by the fact that a game in which your fortune is the number of genes of a particular type in the state of the Markov chain is a fair game.<ref group="Notes" >H. Gonshor, “An Application of | ||
example | |||
just given, the probability of absorption in a state having genes of a | |||
particular type is equal to the proportion of genes of that type in the | |||
starting state. Show that this can be explained by the fact that a game in | |||
which your fortune is the number of genes of a particular type in the state of | |||
the Markov chain is a fair game.<ref group="Notes" >H. Gonshor, “An Application of | |||
Random Walk to a Problem in Population Genetics,” ''American Math Monthly,'' | Random Walk to a Problem in Population Genetics,” ''American Math Monthly,'' | ||
vol. 94 (1987), pp. 668--671</ref> | vol. 94 (1987), pp. 668--671</ref> | ||
Latest revision as of 23:42, 15 June 2024
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Show that in both Example and the example just given, the probability of absorption in a state having genes of a particular type is equal to the proportion of genes of that type in the starting state. Show that this can be explained by the fact that a game in which your fortune is the number of genes of a particular type in the state of the Markov chain is a fair game.[Notes 1]
Notes