# 超几何分布

參數 \begin{align}N&\in 0,1,2,\dots \\ m&\in 0,1,2,\dots,N \\ n&\in 0,1,2,\dots,N\end{align}\, $\scriptstyle{k\, \in\, \max{(0,\, n+m-N)},\, \dots,\, \min{(m,\, n )}}\,$ ${{{m \choose k} {{N-m} \choose {n-k}}}\over {N \choose n}}$ $n m\over N$ $\left \lfloor \frac{(n+1)(m+1)}{N+2} \right \rfloor$ $n(m/N)(1-m/N)(N-n)\over (N-1)$ $\frac{(N-2m)(N-1)^\frac{1}{2}(N-2n)}{[nm(N-m)(N-n)]^\frac{1}{2}(N-2)}$ $\left[\frac{N^2(N-1)}{n(N-2)(N-3)(N-n)}\right]$ $\cdot\left[\frac{N(N+1)-6N(N-n)}{m(N-m)}\right.$ $+\left.\frac{3n(N-n)(N+6)}{N^2}-6\right]$ $\frac{{N-m \choose n} \scriptstyle{\,_2F_1(-n, -m; N - m - n + 1; e^{t}) } } {{N \choose n}} \,\!$ $\frac{{N-m \choose n} \scriptstyle{\,_2F_1(-n, -m; N - m - n + 1; e^{it}) }} {{N \choose n}}$

$f(k;n,m,N) = {{{m \choose k} {{N-m} \choose {n-k}}}\over {N \choose n}}.$