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\end{equation}  Therefore weights proportional to $n_{ti}$ represent a natural choice (see SI XXX).  In general, such a  weighting schemes are scheme is  used for building efficient estimators for a population parameter (e.g. $E_p$). But But,  it canbe  also be  used to build weighted histograms or Kernel Density Estimation (KDE) plots whichwill  exhibit FRET subpopulations with optimal width, yielding more accurate fit of peaks positions and better resolving resolution of  nearby peaks (compared to corresponding non-weighted plots using the same burst-size threshold).  Traditionally,without using weights,  for optimal results, results when not using weights,  the width of FRET subpopulations peaks are manually optimized by finding an ad-hoc (high)   size-threshold which selects only bursts with the highest size (and thus lowest variance).  This procedure, needs to balance reduction in fitting error due to using bigger bursts