

\subsection{\bf 3.1\hspace{1em} Maximum Likelihood Principle}
\subsection{\bf Illustrated by Measurement Errors---I}

\begin{slide}
\begin{itemize}
\item Take the example of a rod quivering in an earthquake

\item $x_1$, $x_2 \ldots x_n$ are $n$ measurements of the length of a rod.

\item Owing to a Gaussian earthquake (or a Gaussian, i.e., normal
drunkenness) occurring during the measurement, the $x_i$ are scattered
about the true value.

\item You visit your favorite theorist (or do it yourself after
sobering up) who {\em believes\/} that the probability distribution of
$x_i$ is Gaussian with mean $\alpha_0 = $ true length and standard
deviation $\sigma_0$.

\item Our superstar knows the value of $\sigma_0$ but not of
$\alpha_0$.

\item We may write down the (relative) probability of each measurement
$x_i$ as:

\[
p_i \left( x_i \right) = c \exp \left\lbrace - \frac{1}{2\sigma^2_0}
\left( x_i - \alpha_0 \right)^2 \right\rbrace
\]
\end{itemize}
\end{slide}

