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3,252 notes

3,252 notes

Negative Binomial · cho.sh

Negative Binomial

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$r \geq 2$

$X - \text{\# of trials until the rth success}$

$x \in \mathbb{Z}^+$

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$x \in \{r, ~r+1, ~r+2, \cdots\}$

P(X=x) = {{x-1} \choose {r-1}} p^{r-1} (1-p)^{x-r} p

Where ${{x-1} \choose {r-1}} p^{r-1} (1-p)^{x-r}$ is the $r-1$ successes out of x-1 trials, and $p$ is the $x$ th trial of $r$ th success.

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