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William P. Gammel edited section_Results_subsection_Muon_Decay__.tex
over 8 years ago
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\section{Results}
\subsection{Muon Decay}
\subsubsection{Mean Lifetime}
A plot of data collected over a five day period can be seen in Figure ~\ref{fig:Muon}. Data for a time in the range of $0-12\mu\textrm{seconds}$ was plotted as a histogram with bin size 60 ns. To increase the accuracy of our expected mean muon lifetime, a few adjustments were made. First the data was trimmed, which slightly increased our calculated value of $\tilde\chi^2$ , indicating a
() better fit for the trimmed result. It should also be noted (refer to Figure ~\ref{fig:Muon}) that fewer decays occurred at high time measurements, and thus the uncertainty on these values were higher. Although it was not done for this experiment, it is possible to weight the data points such that the decays that occurred at higher time measurements are less significant. Mean muon lifetime was taken from a best fit plot which had equation of the form:
\begin{equation}
N(t)=Ae^{\frac{-t}{\tau}}+B
\end{equation}