What is the probability generating function G(s)=E[sX]G(s) = E[s^X]G(s)=E[sX] for X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ)?
eλ(s−1)e^{\lambda(s-1)}eλ(s−1)
eλse^{\lambda s}eλs
(1−p+ps)n(1-p+ps)^n(1−p+ps)n
1/(λ−s)1/(\lambda - s)1/(λ−s)