# hygepdf

Hypergeometric probability density function

## Syntax

```Y = hygepdf(X,M,K,N) ```

## Description

`Y = hygepdf(X,M,K,N)` computes the hypergeometric pdf at each of the values in `X` using the corresponding size of the population, `M`, number of items with the desired characteristic in the population, `K`, and number of samples drawn, `N`. `X`, `M`, `K`, and `N` can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.

The parameters in `M`, `K`, and `N` must all be positive integers, with `N``M`. The values in `X` must be less than or equal to all the parameter values.

The hypergeometric pdf is

`$y=f\left(x|M,K,N\right)=\frac{\left(\begin{array}{c}K\\ x\end{array}\right)\left(\begin{array}{c}M-K\\ N-x\end{array}\right)}{\left(\begin{array}{c}M\\ N\end{array}\right)}$`

The result, y, is the probability of drawing exactly x of a possible K items in n drawings without replacement from a group of M objects.

## Examples

Suppose you have a lot of 100 floppy disks and you know that 20 of them are defective. What is the probability of drawing 0 through 5 defective floppy disks if you select 10 at random?

```p = hygepdf(0:5,100,20,10) p = 0.0951 0.2679 0.3182 0.2092 0.0841 0.0215```

## Version History

Introduced before R2006a