Hi, I am struggling on this problem.
A married couple who prefer girls to boys decide to keep having children until they have one more girl than boy. From different methods, they can guarantee that each time they conceive, the baby's gender is female with probability 2/3 and male with probability 1/3.
Let X be the total number of children they end up having.
I was given that:
with probability 2/3
with probability 1/3.
where are independent random variables each with the same distribution as .
What would be the pdf of this distribution? What would be the best way to find the mean and variance of X?