### 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).

Hmmmmmmm.

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).

Hmmmmmmm.

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