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<h3>Functional relationships for <script type="math/tex">\;\;X \sim H(N,M,K),  \;x=0,1,2,...,K\\ M-(N-K)\leq\;x\leq\;M;\;N,M,K \geq\;0</script>
</h3>
$$
\begin{aligned}
f(x|N,M,K)&=\\frac{\\dbinom{M}{x}\\dbinom{N-M}{K-x}}{\\dbinom{N}{K}}\\\\\\\\
F(x|N,M,K)&=\sum_{i=0}^{x}\\frac{\\dbinom{M}{i}\\dbinom{N-M}{K-i}}{\\dbinom{N}{K}}\\\\\\\\
E[X]&=\\frac{KM}{N}\\\\\\\\
Var[X]&=\\frac{KM}{N}\\frac{(N-M)(N-K)}{N(N-1)}
\end{aligned}
$$
