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Hypergeometric probability density function

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

`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

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

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.

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

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