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@jemoka / Jemoka Knowledge Base / wiki/concepts/negative_binomial_distribution.md
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--- title: "negative binomial distribution" type: concept related: [Probability] source: https://www.jemoka.com/posts/kbhnegative_binomial_distribution/ confidence: high status: active --- how many trials do you need to get r successes. \begin{equation} P(X=n) = {{n-1} \choose {r-1}} p^{r} (1-p)^{n-r} \end{equation} if the chance of individual success is \(p\), what’s the probability that it takes \(n\) trials to get \(r\) successes. \begin{equation} \mathbb{E}[x] = \frac{r}{p} \end{equation} \begin{equation} Var[x] = r \frac{{1-p}}{r^{2}} \end{equation}