
\begin{slide}
\subsection{\bf Example: Estimation of Image}
\subsection{\bf Scanning Efficiency---II}
\begin{itemize}
\item Then, $P(C) = P(A) P(B)$ if we assume scans $A$, $B$ are independent.
\begin{description}
\item{$\bullet$} (in practice {\bf not\/} true as say short tracks or
larger swimsuits would be systematically missed by either graduate or
undergraduates!).
\end{description}
\item Therefore, making independence assumption
\[
\frac{n(C)}{n_{\rm tot}} = \frac{n(A)}{n_{\rm tot}} \cdot 
\frac{n(B)}{n_{\rm tot}}
\]
or
\[
n_{\rm tot} = \frac{n(A) n(B)}{n(C)}
\]
is desired estimate of total number of events.  

\item In practice, second scan will usually only be done on a subset of
data sample.

\item Note if $A$, $B$ {\em independent}
\[ 
P(A/B) = \frac{P(AB)}{P(B)} = P(A)
\]
independent of $B$.
\end{itemize}
\end{slide}

