Computing f(x) for any given x is relatively painless but computing F(x) could take some effort. There is generally not a graphing calculator distribution option for negative binomial but the interactive cells below can be utilized to help with the tedious computations. For example, if you were interested in \(P(X \lt 20) = P(X \le 19 ) = F(19)\) then the interactive calculator below using r=3 and \(p = \frac{1}{12}\) gives \(F(19) \approx 0.20737.\)