# Math Help - Can any one help me?

1. ## Can any one help me?

hi guys.Can any one help me with this Q?

To control the population size and make a somewhat traditional population
happy at the same time, a government passes a law that requires couples to stop having
children once they have a son. Assuming that sons and daughters are equally likely,
the distribution of family size is geometric, with pdf given by
P(M = m) =1/2^m (Geometric distribution)

Interestingly, the average size of the family is 2, so the population size should stabilise. Since the standard deviation is radical 2, most families should have 5 or less children.

So how it got 5 children?

2. Your working thus far is really good.

Now consider the CDF $\displaystyle F(m)= 1-\left(1-\frac{1}{2}\right)^{m}$

Choose values $\displaystyle m=1,2,3,\dots$

You should find $\displaystyle F(5)=0.97$ which is 'most' families.