return the variance of a quantity-with-error
Variance( obj )
The Variance( obj ) command returns the variance of the quantity-with-error obj.
The quantity-with-error obj can have functional dependence on other quantities-with-error.
If the quantity-with-error obj does not have functional dependence on other quantities-with-error, the uncertainty of obj is accessed and converted to the variance (by squaring).
If the quantity-with-error obj has functional dependence on other quantities-with-error, the variance is calculated using the usual formula of error analysis involving a first-order expansion with the dependent form and covariances between the other quantities-with-error. This process can be recursive.
The variance u2⁡y in y, where y depends on the xi, is
where u⁡xi is the error in xi, u⁡xi,xj is the covariance between xi and xj, and the partials are evaluated at the central values of the xi.
Variances involving physical constants are calculated naturally and correctly in the implied system of units because central values and errors are obtained from the interface to ScientificConstants.
a := Quantity( 10., 2. ):
Variance( a );
GetConstant( h );
Variance( Constant( h ) );
GetConstant( m[e] );
Variance( Constant( m[e] ) );
GetError( Constant( m[e] ) )^2;
ScientificErrorAnalysis and ScientificConstants
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