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SangYoon Chung edited Burst_Variance_Analysis.tex
about 8 years ago
Commit id: 41982106d45e5c3408794ff7cafd2773f36f22df
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This is an approximation because background counts (both from sample and detector's dark counts) add additional variance that is not taken into account. However, the approximation works well in practical cases because the background contribution
is normally a small fraction of the total number of counts (therefore it marginally contributes to the variance).
\begin{equation}
\label{eq:binom_dist}
N_a \sim \operatorname{Binom} \{n, E\}
\end{equation}
\begin{equation}
\label{eq:binom_std}
\operatorname{Std(\textit{E})} = {\sqrt{\frac{E(1 - E)}{n}}}