Suppose $X$ has a $Binomial(n,p)$ distribution. Then its moment generating function (MGF) $M_{X}(t)$ is $(pe^t+(1-p))^n$.
But what is the MGF of $-X$, i.e. $M_{-X}(t)=\mathbb{E}(e^{-tX})$?
Is it $M_{-X}(t)$= $(pe^{-t}+(1-p))^n$?
Or should the notation be $M_{X}(-t)$ and let $X$ be positive?