超幾何分布
多変量超幾何分布に従う確率変数を (X1, ..., Xc) とする。
確率質量関数 P  ( X 1 = k 1 , ... , X c = k c ) = 1 ( N n ) ∏ i = 1 c ( K i k i ) {\displaystyle \operatorname {P} (X_{1}=k_{1},\dots ,X_{c}=k_{c})={\frac {1}{\binom {N}{n}}}\prod _{i=1}^{c}{\binom {K_{i}}{k_{i}}}}
期待値 E [ X i ] = n K i N {\displaystyle E[X_{i}]={\frac {nK_{i}}{N}}}
分散 Var  [ X i ] = ( N − n ) n ( N − K i ) K i ( N − 1 ) N 2 {\displaystyle \operatorname {Var} [X_{i}]={\frac {(N-n)n(N-K_{i})K_{i}}{(N-1)N^{2}}}}
共分散 Cov  [ X i , X j ] = − ( N − n ) n K i K j ( N − 1 ) N 2 {\displaystyle \operatorname {Cov} [X_{i},X_{j}]=-{\frac {(N-n)nK_{i}K_{j}}{(N-1)N^{2}}}}