Let $\displaystyle X$ have a Poisson distribution with parameter $\displaystyle m$. Show that
$\displaystyle P(X$ is even$\displaystyle )=(1+e^{2m})/2$
Let $\displaystyle X$ have a Poisson distribution with parameter $\displaystyle m$. Show that
$\displaystyle P(X$ is even$\displaystyle )=(1+e^{2m})/2$
Please help me in solving the problem
for the avoidance of doubt, i assume you are using the standard notation for a poisson distribution, so $\displaystyle m~ \epsilon (0,\infty]$.
if so, the proposition is false. Your solution gives probabability >1 for sufficiently large values of m.
Last edited by SpringFan25; Mar 3rd 2012 at 07:11 PM.