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·       Format:

= Hypergeometric(SubPop,Trials,Pop) = Hypergeometric(D,n,M)

·       Probability mass function:

f(x)=\frac{\left( \begin{array}{c} D \\ x \end{array} \right) \left( \begin{array}{c} M-D \\ n-x \end{array} \right)}{\left( \begin{array}{c} M \\ n \end{array} \right)}

·       Cumulative distribution function:

F(x)=\displaystyle\sum_{i=0}^{\lfloor x \rfloor} \frac{\left( \begin{array}{c} D \\ i \end{array} \right) \left( \begin{array}{c} M-D \\ n-i \end{array} \right)}{\left( \begin{array}{c} M \\ n \end{array} \right)}

·       Parameter restrictions:

 0 < nM, 0 < DM, M > 0. n, M, and D are integers

·       Domain: 

max (0, n + D - M) ≤ x ≤ min (n, D)

·       Mean:

\frac{nD}{M}

·       Mode: 

xm, xm-1

where xm is an integer

\lfloor x_m \rfloor

otherwise

{where} \: x_m=\frac{\big (n+1 \big) \big(D+1 \big)}{M+2}

·       Variance:

\frac{D \big(M-D \big)n}{M^2}

 


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