# Moment generating function constant term

Suppose the moment generating function for a given Poisson distribution is given by F(t).

If I have another weird random variable which I analyze and find that the moment generating function is F(t)+C (where C is just a constant term), is this also a Poisson distribution Random Variable? It has same expectation and variance as the first one.

A moment generating function is $1$ at $t=0$. So if $C\ne 0$ and $F(t)$ is an mgf, then $F(t)+C$ cannot be an mgf.
• You are welcome. Note that if $t=0$, then $E(e^{tX})=E(1)=1$. – André Nicolas Sep 21 '15 at 1:16