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# betapdf

Beta probability density function

## Syntax

```Y = betapdf(X,A,B) ```

## Description

`Y = betapdf(X,A,B)` computes the beta pdf at each of the values in `X` using the corresponding parameters in `A` and `B`. `X`, `A`, and `B` 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 of the other inputs. The parameters in `A` and `B` must all be positive, and the values in `X` must lie on the interval `[0, 1]`.

The beta probability density function for a given value x and given pair of parameters a and b is

`$y=f\left(x|a,b\right)=\frac{1}{B\left(a,b\right)}{x}^{a-1}{\left(1-x\right)}^{b-1}{I}_{\left[0,1\right]}\left(x\right)$`

where B( · ) is the Beta function. The uniform distribution on (0 1) is a degenerate case of the beta pdf where a = 1 and b = 1.

A likelihood function is the pdf viewed as a function of the parameters. Maximum likelihood estimators (MLEs) are the values of the parameters that maximize the likelihood function for a fixed value of x.

## Examples

```a = [0.5 1; 2 4] a = 0.5000 1.0000 2.0000 4.0000 y = betapdf(0.5,a,a) y = 0.6366 1.0000 1.5000 2.1875```

## See Also

### Topics

Introduced before R2006a

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