Expected limits from S/sqrt(B)
mu ~ sqrt(B)/S
proof:
For Expected limit measured signal is
\[ \hat{N}_{S} = 0 \pm \sqrt{B} \]
\[ \hat{\mu} = \hat{N}_{S} / N_{SM} = 0 / S \]
\[ \sigma_{\mu} = \frac{\sigma(N_S)}{N_{SM}} = \frac{\sqrt{B}}{S} \]
mu ~ sqrt(B)/S
proof:
For Expected limit measured signal is
\[ \hat{N}_{S} = 0 \pm \sqrt{B} \]
\[ \hat{\mu} = \hat{N}_{S} / N_{SM} = 0 / S \]
\[ \sigma_{\mu} = \frac{\sigma(N_S)}{N_{SM}} = \frac{\sqrt{B}}{S} \]