I'm stuck in a proof inside a galton watsonn process. My goal is to extimate the variance of $Z_n$, where $Z_n$ is the population at time $n$.
I've already given the extimate of my generating function first and second derivate, but I'm stuck where the paper I'm using says:
Now if $X$ is a nonegative integer valued random variable with probability generating function $g$
35. $EX=g'(1)$
36. $VarX=g''(1)+g'(1)-(g'(1))^2$
whenever the quantities on either side of these equations are finite
Can anyone please explain me where those two equations comes our? Thanks in advance