Two ammeters $A_1$ and $A_2$ measure the same current and provide readings $I_{1}and{I}_2,$ respectively. The ammeter errors can be characterized as independent zero mean Gaussian random variable of standard deviations ${\sigma }_{1}and{\sigma }_2,$ respectively. The value of the current is computed as:



$I=\mu I_1+(1-\mu )I_2$



The value of $\mu$ which gives the lowest standard deviation of I is