# Re: st: product function

 From rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp) To statalist@hsphsun2.harvard.edu Subject Re: st: product function Date Tue, 25 May 2004 12:00:43 -0500

Dimitriy V. Masterov <dvmaster@lily.src.uchicago.edu> asks:

> I would like to plot the probability that two people share a birthday as a
> function of the number of people in the room n. The formula is

> 	1-product((366-i)/365,i,1,n)

> In TeX, it would be

> 	1-\dprod\limits_{i=1}^{n}\frac{366-i}{365}.

> If I have a variable n={1,...,50}, how can I define the product within
> Stata? There does not seem to be math function that can do this.

The product is the exponentiated sum of the logs.

. clear
. set obs 100   // I assume that is enough, p(100) = .9999997
. gen i = _n
. gen p = 1-exp(sum(ln(366-i) - ln(365)))

--Bobby

P.S.  The break-even point on a bet is n = 23 people.

--Bobby
rgutierrez@stata.com
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