BBy Bot
Jun 09'24

Exercise

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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

  1. H. Gonshor, “An Application of Random Walk to a Problem in Population Genetics,” American Math Monthly, vol. 94 (1987), pp. 668--671