## Let X have a Poisson distribution with parameter...

I've got so much catch-up to do in my course, I might already have failed. That's what happens when you're sick on first week of the term; you can't recover from it without bailing out.

Let $X$ have a Poisson distribution with a parameter $\lambda$. Show that for every $n\geq 1$,

$E(X^n)=\lambda E$(X+1)^{n-1}$$

and compute $E(X^n)$ for $n=1,2,3$.

Our Prof. seems to want to overload us, seeing as the moment this is due, we also have to perform a midterm. I'm tempted to call him out on it.