

\subsection{\bf Remarks on Counting Errors}
\subsection{\bf in Moments---II}

\begin{slide}
\begin{itemize}
\item We show this in a model problem in two variables: 

\item $x$ is variable on which moment taken and $y$ is binned.  

\item Choose:
\begin{eqnarray*}
P(x,y) & = & p(y) \frac{\lbrack 1 + \alpha (y) x \rbrack}{2} \\
\mbox{Take a $y$-bin} && y_1 \le y \le y_2 \\
\mbox{set}\ S(y) = 1: && y_1 \le y \le y_2 \\
= 0: && \mbox{otherwise.}
\end{eqnarray*}

\item Assume $\alpha (y)$ is constant at $\alpha$ over bin and then
method of moments is
\[
\alpha = 3\hspace{10pt} \frac{{\displaystyle\sum^{N_T}_{i=1}} f(x_i , y_i 
)}{{\displaystyle\sum^{N_T}_{i=1}} g(x_i , y_i )} = \frac{3F}{G} 
\]

\item where
\begin{eqnarray*}
f(x , y) & = & x S(y) \\
g(x , y) & = & S(y)
\end{eqnarray*}
\end{itemize}
\end{slide}

