Hi, having touble with this moment generating function problem.
I'm given the moment generating function $M_X(t)=\frac {a} {3e^{-t}-2}$ and need to find $a$ and the largest admissible domain for $M_X(.)$.
I know that $M_x(t) = E(e^{tX}) = 1 + tm_1 + \frac{t^2m_2}{2!} + \frac{t^3m_3}{3!} + \ldots +\frac{t^nm_n}{n!} + \ldots$m where $m_n$ is the $n$th moment.