1. Poisson Distribution

Let $X$ have a Poisson distribution with parameter $m$. Show that
$P(X$ is even $)=(1+e^{2m})/2$

2. Re: Poisson Distribution

Let $X$ have a Poisson distribution with parameter $m$. Show that
$P(X$ is even $)=(1+e^{2m})/2$
for the avoidance of doubt, i assume you are using the standard notation for a poisson distribution, so $m~ \epsilon (0,\infty]$.