deletions | additions       diff --git a/Burst_Variance_Analysis.tex b/Burst_Variance_Analysis.tex  index cf853e9..a972ff2 100644  --- a/Burst_Variance_Analysis.tex  +++ b/Burst_Variance_Analysis.tex 
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$E$ is the FRET efficiency. (In practice, Proximity ratio is used as $E$, instead of FRET efficiency) Since, as mentioned, $N_a$ will follow a binomial distribution and $E$ = $N_a$/$n$, we expect the standard deviation of $E$ for the sub-bursts to be distributed according to eq.~\ref{eq:binom_std}. 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}  \sim \operatorname{Binom} \{n, E\}  \end{equation}  \begin{equation}  \label{eq:binom_std}  \operatorname{Std($E$)} = {\sqrt{\frac{E(1 - E)}{n}}}  \end{equation}  BVA analysis consists of four steps: 1) slicing bursts into sub-bursts containing \textit{n} consecutive photons, 2) computing FRET efficiencies of each sub-burst, 3) calculating the empirical standard deviation ($s_E$) of sub-burst FRET efficiencies over the whole burst, and 4) comparing $s_E$ to an expected standard deviation based on shot noise limited distribution~\cite{Torella_2011}.