Variance

Uniform distribution variance.

The variance for a uniform random variable is

upper V a r left-parenthesis upper X right-parenthesis equals one-ttwelfth left-parenthesis b minus a right-parenthesis squared

where a is the minimum support and b the maximum support of the distribution.

Usage

var variance = require( '@stdlib/math/base/dists/uniform/variance' );

variance( a, b )

Returns the variance of a uniform distribution with parameters a (minimum support) and b (maximum support).

var v = variance( 0.0, 1.0 );
// returns ~0.083

v = variance( 4.0, 12.0 );
// returns ~5.333

v = variance( 2.0, 8.0 );
// returns 3.0

If provided NaN as any argument, the function returns NaN.

var v = variance( NaN, 2.0 );
// returns NaN

v = variance( 2.0, NaN );
// returns NaN

If provided a >= b, the function returns NaN.

var y = variance( 3.0, 2.0 );
// returns NaN

y = variance( 3.0, 3.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var variance = require( '@stdlib/math/base/dists/uniform/variance' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    v = variance( a, b );
    console.log( 'a: %d, b: %d, Var(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}