Math Help Forum: poisson distribution

Let X have a Poisson distribution with parameter λ. Show that P[X is even] = (1+e^2λ)/2

Originally Posted by jayantamath

Let X have a Poisson distribution with parameter λ. Show that P[X is even] = (1+e^2λ)/2

Substitute x = 2n into the pmf and sum over n (you will need to recognise a standard power series).

If you need more help, please show all your working and say where you get stuck.