
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?

Your working thus far is really good.
Now consider the CDF $\displaystyle \displaystyle F(m)= 1\left(1\frac{1}{2}\right)^{m}$
Choose values $\displaystyle \displaystyle m=1,2,3,\dots$
You should find $\displaystyle \displaystyle F(5)=0.97$ which is 'most' families.