# 超幾何分布

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

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