The general form for the pmf of X = number of children born upto and including the first boy is

p(x) = p * (1-p)^(x-1) where x = 1,2,3,/......

and p(x) = 0 otherwise

find the expected value E(X).

Okay,so this is an example from the book.But what I dont really get is why are they differentiating the p(x) inside the summation.