Antonino Ingargiola edited Burst_Weights_Theory.tex  about 8 years ago

Commit id: dba9b0b6bfbbeae059e8e8fc969dc4e17bf606e4

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\hat{E} = \frac{\sum_i n_{ai}}{\sum_i n_{ti}}  \end{equation}  The variance of $\hat{E}$ (eq.~\ref{eq:E_var}) (eq.~\ref{eq:E_variance})  is equal to the inverse of the Fisher information $\mathcal{I}(\hat{E})$ and therefore $\hat{E}$ is a MVUB   estimator for $E_p$.  \begin{equation}  \label{eq:E_var}  \operatorname{Var}(\hat{E}) = \frac{E_p (1 - E_p)}{\sum_i n_{ti}} \label{eq:E_variance}  \frac{1}{\mathcal{I}(\hat{E})}  \end{equation}  With simple algebra is verify that $\hat{E}$ is equal to the weighted average of the bursts