Changes between Version 75 and Version 76 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/05/19 09:13:11 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -32 +32 @@
 Assuming Gaussian errors, the statistical error is thus
 
-\[\sigma^2(N_\textrm{exc}) = \left(\frac{dN_\textrm{exc}}{dN_\textrm{sig}}\right)^2\sigma^2(N_\textrm{sig}) +  \left(\frac{dN_\textrm{exc}}{d\hat N_\textrm{bg}}\right)^2\sigma^2(\hat N_\textrm{bg}) = N_\textrm{sig} + \frac{1}{5^2}N_\textrm{bg} \]
+\[\sigma^2(N_\textrm{exc}) = \left(\frac{dN_\textrm{exc}}{dN_\textrm{sig}}\right)^2\sigma^2(N_\textrm{sig}) +  \left(\frac{dN_\textrm{exc}}{d\hat N_\textrm{bg}}\right)^2\sigma^2(\hat N_\textrm{bg})\]
+
+For data this immediately resolves to 
+
+\[\sigma^2(N_\textrm{exc}) = N_\textrm{sig} + \frac{1}{5^2}N_\textrm{bg} \]
+
+assuming \(\sigma^2(N_\textrm{sig,bg}) = N_\textrm{sig,bg}\).