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16 Sep 2004 06:50 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
firecatDoes your iTunes randomizer have favorite songs? I have over 3000 songs in mine, and this one has come up at least once a day over the past week.
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firecat (attention machine in need of calibration)
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Date: 17 Sep 2004 02:32 pm (UTC)What is the expected number of songs which will have been played ten or more times over the course of a week?
What is the expected number of songs that won't have been played at all in a week?
These are calculable numbers.
A quick-and-dirty handwaving kluge would be to figure that there are 7*24*60/3 = 3360 timeslots to fill with 3000 songs, so that the expected number of times a single song was played is 1.12, and plug it into the Poisson distribution.
Results left as an exercise to the student, who might turn out to be surprised.
I just did the math
Date: 17 Sep 2004 03:13 pm (UTC)Expected number of songs never played: 978.84
Expected number of songs played once: 1096.3
Played twice: 613.93
Played thrice: 229.2
Four times: 64.18
Five times: 14.38
Six times: 2.68
Seven times: 0.43
Eight times: 0.06
Nine times: 0.01
Ten times : 0.00
We'd expect to hear between either two or three songs played six times over the course of the week. There is a 43% chance that there is one song played (on average) every day.
This has been an obsessive-compulsive moment.
Re: I just did the math
Date: 20 Sep 2004 05:33 pm (UTC)(I would have said so sooner, but there's no net access on the Mendocino County coast.)