

\subsection{\bf Remarks on Counting Errors}
\subsection{\bf in Moments---I}
\begin{slide}
{\Smallsize
\begin{itemize}
\item In formula
\begin{equation}
\langle f\rangle = \frac{{\displaystyle\sum^N_{i=1}} f(x_i)}{N}
\end{equation}
\item I used to worry if you should include counting error $(\sqrt{N})$
in $N$ in error estimate which otherwise only involves the Standard
Deviation of $f$.  
\item If $N$ is a priori fixed, clearly there is no $\sqrt{N}$ error
but suppose the events used in Equation~(26) are those that fall in a
particular subregion (counter) of a bigger sample space (and $f(x)$ is
defined only over this subregion).
\item Then the estimate of probability of falling into counter
certainly involves $\sqrt{N}$ error!  What about the mean of a quantity
within subregion---does this involve this error?
\item The problem is:  what is error in a moment:  should it include
counting error?  
\item The answer is no---one uses identical formulae in
case where number of events prescribed and not subject to counting
error.
\end{itemize}
}
\end{slide}

