Question

Three brothers and their wives decide to have children until each family has two female children. What is the pmf of X = total number of male children born to the brothers? What is the E(X), and how does it compare to the expected number of male children born to each brother?

Answer 1

I set up the negative binomial to look like this: nb(x; 6, p)

and the pmf like this:

\[\left(\begin{matrix}6 + x - 1 \\ 6-1\end{matrix}\right)p ^{6}(1-p)^{x}\]

But this is as far as I was able to go. I don't know if I should be assuming a probability here or something.