

\begin{slide}
\subsection{\bf Properties of Gaussian Distribution}
\begin{itemize}

\item Note that we have ensured in Equation~(4) that
\[
\int\limits^{+\infty}_{-\infty} p(x) dx = 1
\]

\item Also, the associated distribution function is:
\[
F(x) = \Phi (x) = \frac{1}{\sqrt{2\pi} \sigma} {\displaystyle 
\int\limits^x_{-\infty}} dy \exp \left\lbrack - 
\frac{(y-\mu)^2}{2\sigma^2}\right\rbrack
\]

\item which cannot be done analytically except by relating it to the
error integral:
\[
{\rm erf}(x) = \frac{2}{\sqrt{\pi}} \int\limits^x_0 \exp \left( -y^2 \right) dy
\]
\end{itemize}
\end{slide}

