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# Mean
> [Triangular][triangular-distribution] distribution [expected value][expected-value].
<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
<section class="intro">
The [mean][expected-value] for a [triangular][triangular-distribution] random variable is
<!-- <equation class="equation" label="eq:triangular_mean" align="center" raw="\mathbb{E} \left[ X \right] = \frac{a+b+c}{3}" alt="Mean for a triangular distribution."> -->
<div class="equation" align="center" data-raw-text="\mathbb{E} \left[ X \right] = \frac{a+b+c}{3}" data-equation="eq:triangular_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/triangular/mean/docs/img/equation_triangular_mean.svg" alt="Mean for a triangular distribution.">
<br>
</div>
<!-- </equation> -->
where `a` is the lower limit, `b` is the upper limit and `c` is the mode.
</section>
<!-- /.intro -->
<!-- Package usage documentation. -->
<section class="usage">
## Usage
```javascript
var mean = require( '@stdlib/stats/base/dists/triangular/mean' );
```
#### mean( a, b, c )
Returns the [expected value][expected-value] of a [triangular][triangular-distribution] distribution with parameters `a` (minimum support), `b` (maximum support), and `c` (mode).
```javascript
var v = mean( 0.0, 1.0, 0.8 );
// returns ~0.6
v = mean( 4.0, 12.0, 5.0 );
// returns 7.0
v = mean( 2.0, 8.0, 5.0 );
// returns 5.0
```
If provided `NaN` as any argument, the function returns `NaN`.
```javascript
var v = mean( NaN, 4.0, 2.0 );
// returns NaN
v = mean( 0.0, NaN, 2.0 );
// returns NaN
v = mean( 0.0, 4.0, NaN );
// returns NaN
```
If provided parameters not satisfying `a <= c <= b`, the function returns `NaN`.
```javascript
var y = mean( 1.0, 0.0, 1.5 );
// returns NaN
y = mean( 0.0, 1.0, -1.0 );
// returns NaN
y = mean( 0.0, -1.0, 0.5 );
// returns NaN
```
</section>
<!-- /.usage -->
<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
<section class="notes">
</section>
<!-- /.notes -->
<!-- Package usage examples. -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var randu = require( '@stdlib/random/base/randu' );
var mean = require( '@stdlib/stats/base/dists/triangular/mean' );
var a;
var b;
var c;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
a = ( randu()*10.0 );
b = ( randu()*10.0 ) + a;
c = ( randu()*( b-a ) ) + a;
v = mean( a, b, c );
console.log( 'a: %d, b: %d, c: %d, E(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
}
```
</section>
<!-- /.examples -->
<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
<section class="references">
</section>
<!-- /.references -->
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
<section class="links">
[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution
[expected-value]: https://en.wikipedia.org/wiki/Expected_value
</section>
<!-- /.links -->
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