If X∼Binomial(n,p)X \sim Binomial(n, p)X∼Binomial(n,p), what is the probability generating function GX(s)=E[sX]G_X(s) = E[s^X]GX(s)=E[sX]?
(ps+1−p)n(ps + 1 - p)^n(ps+1−p)n
eλ(s−1)e^{\lambda(s-1)}eλ(s−1)
ps1−(1−p)s\frac{ps}{1-(1-p)s}1−(1−p)sps
sns^nsn