Expected limits from S/sqrt(B)

mu ~ sqrt(B)/S

proof:

For Expected limit measured signal is

\[ \hat{N}_{S} = 0 \pm \sqrt{B} \]

\[ \hat{\mu} = \hat{N}_{S} / N_{SM} = 0 / S \]

\[ \sigma_{\mu} = \frac{\sigma(N_S)}{N_{SM}} = \frac{\sqrt{B}}{S} \]