\subsection{ Accept-Reject Methods  for Event Generation---II}


\begin{itemize}
\item An Alternative is to use acceptance-rejection to find a set $M$
of events $j$ with ``weight 1.''  Then
\begin{equation}
\langle Q\rangle = \frac{1}{M} \sum^M_{j=1} q_j
\end{equation}

\item When is Equation~(39) superior to Equation~(38)?

\item If you are just calculating $\langle Q\rangle$, then (38)
contains all the information you have and is ``best.''  

\item However, if you are doing a lot of work to calculate $q_i$, 

\begin{description}
\item{$\bullet$} or maybe there are many different quantities $q_i$, 
\item{$\bullet$} the accept-reject technique is best.
\end{description}

\item Thus, it is clearly a waste to spend a lot of time calculating
$q_i$ for an event whose weight $w_i$ is small, e.g., 0.001
$w_{\max}$!
\end{itemize}