Work out negative binomial distribution instantly with clear inputs, formula shown and shareable results.
The negative binomial gives the probability that the rth success falls exactly on trial n: C(n−1, r−1)pʳ(1−p)^(n−r). Its mean r/p reflects that each success takes 1/p trials on average.
Negative binomial pmf
P(X = n) = C(n−1, r−1)·pʳ·(1−p)^(n−r)
Mean and variance
E = r/p, Var = r(1−p)/p²
P ≈ 0.0800, and 3 successes are expected to take about 10 trials.
The binomial fixes the trial count and counts successes; the negative binomial fixes the success count and counts trials.