probability generating function of a poisson random variable
i should start by asking is anyone on the forum well versed in the coalescent theory?
i have a problem in a derivation
if the number of mutations is given by
as one can see this is the probability generating function of a poisson random variable with random mean. where
now from here i can write this as a product
Now im confused what to do. If i have the probability generating function how do i find the density function (derivative?)
the next step in the derivation should be
I cant for the life of me figure out how this was found from the pgf. PLEASE ANY IDEAS ARE WELCOME, SO IF NO ONE KNOWS THE ANSWER SUGGEST ANYTHING.