In this post, we discuss a new file uploaded.

Mean/Variance of Negative Binomial

I was asked the other day to calculate the mean/variance of negative binomial. I have known the trick of using linearity for calculating these things for binomial variables, but I didn’t see a way of repeating it for this case (Wikipedia mentions a way, but I didn’t put much thought into it). Most of the proofs I saw used moment generating functions, which is fine but I think it’s a little overkill. It turns out there’s a pretty elementary way of doing it using just some facts on binomial coefficients, which is easy enough to prove. I have posted it here.