Mean Deviation about mean for Poisson Distribution?

• Is this the "mean absolute deviation" or the "mean square deviation"?
– mlc
Apr 29 '17 at 11:12

For the absolute mean deviation of $X \sim Poi(\lambda)$,
$$\mathbf{E}_\lambda|X - \lambda| = 2\frac{e^{-\lambda}\lambda^{[\lambda]+1}}{[\lambda]!} = 2 \lambda \mathbf{P}_\lambda(X = [\lambda])$$
where $[\lambda]$ is the integer part of $\lambda$. Here is a quick reference for this kind of results, and here is the original proof if you are interested.