Recursions for the Moments of Some Discrete Distributions

You could say, "Moments maketh the distribution". While that's not quite true, it's pretty darn close.

The moments of a probability distribution provide key information about the underlying random variable's behaviour, and we use these moments for a multitude of purposes. Before proceeding, let's be sure that we're on the same page here.

Sums of Random Variables

I'm currently teaching first-level course in statistical inference for  (mostly) economics students. They've taken a one-semester course in descriptive (economic) statistics, and now we're dealing with sampling distributions, estimation, hypothesis testing, and simple regression analysis.