

\subsection{\bf Generation of Gaussian}
\subsection{\bf Random Numbers---I}
\begin{slide}
\begin{itemize}

\item Gaussian Random Numbers can be generated by:
\[
g = \frac{{\displaystyle\sum^N_{i=1}} u_i - \frac{N}{2}}{\sigma\sqrt{N}}
\]

\item where $\sigma^2 = 1/12$ and $u_i$ are uniformly distributed
between 0 and 1, is Gaussianly distributed for large $N$.  

\item This, for $N\sim 10$ is sometimes used in computers.  

\item More convenient is often
\begin{eqnarray*}
g_1 & = & (-2\ln u_1)^{\frac{1}{2}} \cos 2\pi u_2 \\
g_2 & = & (-2\ln u_1)^{\frac{1}{2}} \sin 2\pi u_2 
\end{eqnarray*}
where $u_i$ are uniform in [0,1] and then $g_i$ are independent random
numbers which are Gaussianly distributed with zero mean and unit
variance.
\end{itemize}
\end{slide}

