# Documentation

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# 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 NM. 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