

\subsection{\bf Examples of Correlations}
\subsection{\bf 2D Track Finding---I}

\begin{slide}
\begin{enumerate}
\item {\em Measurement of Tracks in Chambers}
\end{enumerate}

\vspace*{10pt}
\centerline{\psfig{figure=fig4.phys.ps,clip=true,width=5.5in}}
\vspace*{10pt}

\begin{itemize}
\item Track is $x=a+bz$ ($a=$intercept, $b=$ slope), where
\begin{eqnarray*}
b & = & \frac{\left( x_2 - x_1 \right)}{\left( z_2 - z_1 \right)} \\
a & = & \frac{z_2 x_1 - z_1 x_2}{z_2 - z_1}
\end{eqnarray*}

\item $x_i$ are measured as {\em independent\/} random variables, but
the combinations $a$ and $b$ are clearly correlated.

\[
\left\langle (b-\langle b\rangle ) (a - \langle a\rangle ) \right\rangle = 
- \frac{z_2 \sigma^2_1 - z_1 \sigma^2_2}{\left( z_1 - z_2 \right)^2}
\]

\item where $x_i$ has standard deviation $\sigma_i$.  
\end{itemize}
\end{slide}

