Let XXX have MGF MX(t)=(1−t)−kM_X(t) = (1-t)^{-k}MX(t)=(1−t)−k for t<1t<1t<1. What is the distribution of XXX?
Gamma(k,1)\text{Gamma}(k, 1)Gamma(k,1)
Exponential(k)\text{Exponential}(k)Exponential(k)
Poisson(k)\text{Poisson}(k)Poisson(k)
Binomial(k,0.5)\text{Binomial}(k, 0.5)Binomial(k,0.5)