Let X∼Gamma(α,β)X \sim \text{Gamma}(\alpha, \beta)X∼Gamma(α,β). Which of the following is the moment generating function MX(t)M_X(t)MX(t)?
(1−t/β)−α(1 - t/\beta)^{-\alpha}(1−t/β)−α
(1−βt)−α(1 - \beta t)^{-\alpha}(1−βt)−α
eαte^{\alpha t}eαt
(1−t/β)α(1 - t/\beta)^{\alpha}(1−t/β)α