9464

An Increasing Preference Distribution

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.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics



 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+