.. _variables-hypergeometric_uncertain-selected_population:

"""""""""""""""""""
selected_population
"""""""""""""""""""


Distribution parameter for the hypergeometric distribution describing the size of the population subset of interest



.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* INTEGERLIST


**Description**


The density function for the hypergeometric distribution is given by:

.. math:: f(x) = \frac{\left(\begin{array}{c}m\\x\end{array}\right)\left(\begin{array}{c}{N-m}\\{n-x}\end{array}\right)}{\left(\begin{array}{c}N\\n\end{array}\right)}

where the three distribution parameters are:

- N is the total population
- *m is the number of items in the selected population* (e.g. the number of white balls in the full urn of N items)
- n is the size of the sample drawn (e.g. number of balls drawn)

In addition,

- x, the abscissa of the density function, indicates the number of successes (e.g. drawing a white ball)
- :math:`\left(\begin{array}{c}a\\b\end{array}\right)`  indicates a binomial coefficient ("a choose b")