

\subsection{\bf Robust Determination of Mean---II}

\begin{slide}
\begin{itemize}
\item Further, the method is unbiased for any $N$, i.e.,
\[
\langle \mu^*_{Am} \rangle = \mu
\]

\item If the $x^{(i)}$ are distributed according to either the

\item Gaussian
\[
p(x) \propto \exp \left( - \frac{(x-\mu)^2}{2\sigma^2} \right)
\]
\item or exponential form
\[
p(x) \propto \exp \left( - \frac{x}{\mu} \right)
\]

\item then we know from maximum likelihood method that the arithmetic
mean is the best method.

\item However, for other distributions, the arithmetic
mean is unlikely to be best.  
\end{itemize}
\end{slide}

