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 variables 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
- $\frac{\sigma^2_2}{\sigma_1^2+\sigma_2^2}$
- $\frac{\sigma_1^2}{\sigma_1^2+\sigma_2^2}$
- $\frac{\sigma_2}{\sigma_1+\sigma_2}$
- $\frac{\sigma_1}{\sigma_1+\sigma_2}$