If X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ), what is the moment generating function MX(t)M_X(t)MX(t)?
eλ(et−1)e^{\lambda(e^t - 1)}eλ(et−1)
eλte^{\lambda t}eλt
eλ(t−1)e^{\lambda(t-1)}eλ(t−1)
1+λt1 + \lambda t1+λt