Find distribution function through moment generating function Suppose that the moment generating function $M_X$$(t)$ of a random variable $X$ is given by 
$$  M_X(t)=\frac{e^t+e^{-t}}{6} + \frac 23 $$
I need to find the distribution function $F_X(x)$.
Until now, I have been given (in my lecture notes) that I can express $E(X)$= $M_X^{(1)}(0)$ . But I can't use this here for finding the distribution function $F_X(x)$?(Or at least I have no idea how to do it) Could you please tell me how to proceed?

Hint: From the moment generating function we can determine the distribution of $X$, which is $P(X=1)=P(X=-1)=\frac16$, $P(X=0)=\frac23$. I believe that you can move on now. 
