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.
Best Answer
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.