My textbook did the derivation for the binomial distribution, but omitted the derivations for the Negative Binomial Distribution.
I know it is supposed to be similar to the Geometric, but it is not only limited to one success/failure. (i.e the way I understand it is that the negative binomial is the sum of independent geometric random variables). For example: $Y_1 +Y_2 +Y_3+\cdots $ where $Y_i$ is a geometric parameter. I can't seem to find online one for the negative binomial and am having trouble with even doing the geometric.
Can anyone show me a derivation of the negative binomial?
Edit: My book calls the negative binomial as the distribution of the number of trials needed to get a specified number r of successes.