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\subsection{Burst Weights}  \label{sec:burstweights_theory}  \subsubsection{Theoretical Foundation}  Freely-diffusing molecules across   a Gaussian excitation volume give rise to   a burst size distribution that is exponentially distributed.  In homogeneous a static  FRET population, burst counts in the acceptor channel can be modeled as a binomial random variable (RV) with success probability equal to the  population PR and number of trials equal to the burst size $n_d + n_a$.  Similarly, the PR of each burst $E_i$ ($i$ being the burst index) is   simply a binomial divided by the number of trials, therefore the with  variance is: reported  in eq.~\ref{eq:E_var}.  \begin{equation}  \label{eq:E_var}  \operatorname{Var} (E_i) = \frac{E_p\,(1 - E_p)}{n_{ti}}  \end{equation}  For a single FRET population, freely-diffusing molecules across   a Gaussian excitation volume give rise to   a burst size distribution that is exponentially distributed.  From eq.~\ref{eq:E_var} we see that bursts Bursts  with larger burst size  will yield higher counts carries a  more accurate estimations of the population PR (since since  their variance will be smaller). smaller.  Therefore, in estimating the population PR we need to "focus" on larger bigger  bursts. Traditionally, this is accomplished by merely discarding bursts  below a size-threshold.  In the following paragraphs we demonstrate how, by proper weights weighting  bursts, is possible to obtains better optimal  estimates by taking of PR which takes  into account the information of the entire burst population.  According to the Cramer-Rao lower bound (eq.~\ref{eq:cramer_rao}), the