

\subsection{\bf Maximum Likelihood Estimate of}
\subsection{\bf Error in Lifetime---II}

\begin{slide}
\begin{itemize}
\item Then we found $L$ became Gaussian in $\tau$, and calling maximum
likelihood standard deviation $\tilde\sigma$
\[
L(\tau) \propto \exp \left\lbrace - \frac{1}{2\tilde{\sigma}^2}
(\tau - \tau^*)^2 \right\rbrace
\]

\item where we can find width $\tilde\sigma$---width of Gaussian by:
\begin{eqnarray} 
\frac{1}{\tilde{\sigma}^2} & = & - \frac{d}{d\tau^2} \ln L(\tau)
\big\vert_{\tau=\tau^*} \nonumber \\
& = & \frac{2}{\tau^3} \sum^n_{i=1} t_i - \frac{n}{\tau^2}
\big\vert_{\tau=\tau^*} \hspace{1em} \mbox{or} \nonumber \\
\tilde\sigma & = & \frac{\tau^*}{\sqrt{n}} 
\end{eqnarray}

\item as $\tau^* = \tau_0 + O \left( \frac{1}{n} \right)$ we see that
Equation~(15) and (16) are in fact the same asymptotically (large $n$,
that is).
\end{itemize}
\end{slide}

