A little context, here is the problem I am working on:
For a random variable X, let g(X) be given by g(X) = abs(X - m(X)), where m(X) is the median of X. Find g(X) for a Poisson random variable with mean 1.5.
So the easy part: the median for this X is 1, so g(X) = abs(X-1). If this were a continuous random variable, I'd integrate and be done with it, but Poisson is discrete.
Is it the case that E(|X-1|) = sum(p(x)*|x-1|)?
Thanks.