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

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

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

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.