deletions | additions       diff --git a/Burst_Weights_Theory.tex b/Burst_Weights_Theory.tex  index bc1bf8a..0939df8 100644  --- a/Burst_Weights_Theory.tex  +++ b/Burst_Weights_Theory.tex 
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using the burst size as weights and fitting the peak is equivalent to using  the MVUB estimator for $E_p$.  \subsubsection{Simulations}  It is easy to illustrate the results of previous section through simulations.  In particular we generate a static FRET population of bursts extracting sizes   from an exponential (or gamma) distribution and acceptor counts from a binomial  distribution. By repeatedly fitting the population parameter $E_p$ using a   size-weighted and unweighted average, we verified that the former has systematically  lower variance of the latter as predicted by the theory. Note that this result  holds for any arbitrary distribution of burst sizes.  \subsubsection{Experiments}  Figure X show a comparison of a FRET histogram obtained from the same burst  with and without weights. The burst selection is obtained applying a burst size  of threshold of 20 counts, in order to filter the extreme low-end of the burst size  distribution which include background bursts.  The use of size-weighted FRET histograms allows to obtain a minimal with of  the various FRET peaks without the need of using a manually adjusted high  threshold for burst selection. While an increase in the selection threshold  reduces the shot-noise of the residual population it also discards the useful   information of low and medium size bursts. Necessarly, an unweighted histograms  with high selection threshold will exhibit an higher statistical noise  (due to the reduced number of bursts) compared to the size-weighted histogram  obtained using a low threshold.  statistical variance