

\subsection{\bf Counter Physics---Introduction}
\subsection{\bf and Poisson Process---II}

\begin{slide}
\begin{itemize}
\item This follows from our theory of Birth processes.  In high energy
physics, $\lambda_i$ is proportional to
${\displaystyle\int_{\mbox{\small BIN}}} dt \frac{d\sigma}{dt}$ where
{\small BIN} is $t$-bite covered by counter ($t$ the momentum transfer
is a particular kinematic range---not time!).

\item The analysis is a straightforward application of maximum
likelihood method:
\begin{equation}
p_i = e^{-\lambda_i t} \frac{(\lambda_i t)^{n_i}}{n_i!}
\end{equation}

\item ($n_i$ observed counts, $\lambda_i$ theory: $t$---now time!---may
be known or not).
\begin{eqnarray}
L & = & \prod^M_{i=1} p_i \hspace{2em} \mbox{or} \nonumber \\
&& \nonumber \\
\ln L & = & - \sum^M_{i=1} \ln n_i! - t \sum^M_{i=1} \lambda_i +
\sum^M_{i=1} n_i \ln (\lambda_i t)
\end{eqnarray}
\end{itemize}
\end{slide}

