

\subsection{\bf Parameters of a}
\subsection{\bf Gaussian Distribution---I}

\begin{slide}
\begin{itemize}
\item Suppose $x$ is Gaussian, i.e.,
\[
p(x) = \frac{1}{\sqrt{2\pi} \sigma} \exp \left\lbrace - \frac{[x-\mu ]^2}{2
\sigma^2}\right\rbrace
\]

\item Then the mean is given by
\begin{eqnarray*}
\langle x\rangle & = & \int\limits^{+\infty}_{-\infty} x\, p(x) dx \\
& = & \mu + \int\limits^{+\infty}_{-\infty} (x-\mu) p(x) dx \\
& = & \mu
\end{eqnarray*}
at last integral clearly vanishes from antisymmetry.  

\item So, fundamental parameter, $\mu$, in Gaussian is just the mean.
\end{itemize}
\end{slide}

