Monday, April 24, 2006

Doing it

I was wondering (call me perverted if you want), at any minute, whats the chance some couple is doing it in a community? Actually, my mind wandered off to "what is the size of polulation (in units of "number of sexually active couples") to say with a confidence of (say) 90% that at least one couple is doing it" - you know similar to that other problem of "how many people must be present in a room in order to say with 90% confidence that at least two poeple share thier birt day".

So this looks like something nicely modeled using poisson distribution.

I modeled it like this, the probability that "at least some couple is doing it" is actually 1 - "probability that no couple is doing it". I also assumed that an average couple does it between 4 and 10 times a month - and add to this the fact that there are 30 * 24 * 60 minutes in a month, you get the rate parameter for the poisson distribution.

It all boils down to at least (ln(1/(1-0.9)) * 30 * 24 * 60)/4 (when its 4 times a month) and (ln(1/(1-0.9)) * 30 * 24 * 60)/10 (when its 10 times a month). (Where ln(x) is the natural logarithm of x (log to the base e)).

Hold you breath:

Its about 24867 and 9947.

That is, if there were 24897 (9947) couples doing it 4 (10) times a month living in a community, then at any minute, you can say with 90% confidence (10 % chance of being wrong - odds of 1 to 9), thaty at least some couple is doing it (Assuming that couples do it at any moment that strikes their fancy, completely randomly).




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