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 $m~ \epsilon (0,\infty]$.

if so, the proposition is false. Your solution gives probabability >1 for sufficiently large values of m.

3. ## Re: Poisson Distribution

Ya the question was wrong, though the same question was set in an university exam. Anyway, I think it will be e^{-2m} in place of e^{2m}