An Increasing Preference Distribution

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Suppose your music player contained songs and you set it to shuffle songs, giving increasing preference to a song each time it was played. That is, initially, all songs are equally likely to be chosen but every time a song is played, its probability of being selected for the next play goes up in such a way that the probability of it being selected is proportional to the number of times it has been played. What would happen over a large number of plays? Would all your songs remain about equally likely or would a few dominant favorites emerge? Investigate this using this Demonstration.

Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA


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If there are songs, then for the first selection, each song is given equal probability . If song is selected for the first play, then song has probability of being selected for the second play while all other songs have probability of being selected. After plays, suppose the song has been played times. Then for the play, it has probability of being selected.



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