# [R] family question

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Wed Aug 30 22:57:57 CEST 2000

```Douglas Bates <bates at stat.wisc.edu> writes:

> Troels Ring <tring at mail1.stofanet.dk> writes:
>
> > Dear friends. Please see the program below and answer if it does simulate a
> > population of 1.000.000 families, each with at max 20000 children (typical
> > in Denmark, you know), constructed such that each family stops having
> > children when more boys than girls are present ? Equal numbers of boys and
> > girls are got in the population, according to the simulation, is that obvious ?
>
> I am not an expert in probability or in stochastic processes so I
> can't say that it is "obvious".  I can say it is not unreasonable if
> you consider the sizes of families.  Basically what happens is that
> large families have nearly equal numbers of girls and boys and also
> have a high weight in the calculation of the population proportion.
> (You can only get odd numbered family sizes according to your rule and
> for a family of size 2K + 1 there will be K girls and K + 1 boys.)

I think it's a variant of the "quit while you're ahead" strategy of
gambling theory, where you show that the mean is 0 except if you have
infinite resources. I.e. if you continue long enough, you will
eventually reach a positive sum, but there is no bound to how deep in
debt you'll be on the way.

So, in the present example you will reach the maximum of 20000 in a
few cases and those cases will have enough extra girls to compensate
for the excess boys in the other families. (20000? I know that winter
nights in Jutland can be boring, but this is ridiculous...)

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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```