7.4.4 A developing country is attempting to control its population growth by placing restrictions on the number of children each family can have. This society places a high premium on female children, and it is felt that any policy that ignores the desire to have female children will fail. The proposed policy is to allow any married couple to have children up to the first female baby, at which point they must cease having children. Assume that male and female children are equally likely. The number of children in any family is a random variable N.

In the population as a whole, what fraction of children are female? Use the elementary renewal theorem to justify your answer