

\subsection{\bf (i) Example from Histogramming}
\subsection{\bf (Physics) Events---I}

\begin{slide}
\begin{itemize}
\item Suppose we select a sample of events from some set,

\item e.g., the sample may be those falling into some bin of a
histogram.

\item We wish to estimate fraction of events with given property.

\item Define random variable $f$ by
\[
\begin{array}{rl}
f = 1 & \hspace{1em} \mbox{event passes selection criteria} \\
= 0 & \hspace{1em} \mbox{event fails criterion.} \\
\end{array}
\]

\item Write $f=\theta g$
\begin{description}
\item{$\bullet$} $g=1$ \hspace{1em} Event in Given Histogram
\item{$\bullet$} $g=0$ \hspace{1em} Event Not in Histogram
\end{description}

\item $\theta$ is only defined for events that fall in histogram, and
\begin{description}
\item{$\bullet$} $\theta=1$ event in particular bin
\item{$\bullet$} $\theta=0$ event does not fall in bin
\end{description}

\item Let $\langle\theta\rangle=p$, and $\langle f\rangle = p\langle
g\rangle$
\end{itemize}
\end{slide}

