# Erl: Hypergeometric Distribution In Distributacalcul: Probability Distribution Functions

## Description

Hypergeometric distribution where we have a sample of k balls from an urn containing N, of which m are white and n are black.

## Usage

 ```1 2 3``` ```expValErl(N = n + m, m, n = N - m, k) varErl(N = n + m, m, n = N - m, k) ```

## Arguments

 `N` Total number of balls (white and black) in the urn. N = n + m `m` Number of white balls in the urn. `n` Number of black balls in the urn. Can specify n instead of N. `k` Number of balls drawn from the urn, k = 0, 1, ..., m + n.

## Details

The Hypergeometric distribution for N total items of which m are of one type and n of the other and from which k items are picked has probability mass function :

((m)C(k) (n)C(k - x)) / ((N)C(k))

for x = 0, 1, ..., min(k, m).

## Value

Function :

• `expValErl` gives the expected value.

• `varErl` gives the variance.

Invalid parameter values will return an error detailing which parameter is problematic.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# With total balls specified expValErl(N = 5, m = 2, k = 2) # With number of each colour of balls specified expValErl(m = 2, n = 3, k = 2) # With total balls specified varErl(N = 5, m = 2, k = 2) # With number of each colour of balls specified varErl(m = 2, n = 3, k = 2) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.