

\subsection{\bf Unnormalized Counter Experiment---II}

\begin{slide}
\begin{itemize}
\item or dropping terms independent of $\lambda_i$ :
\begin{eqnarray}
\ln L & = & \sum^M_{i=1} n_i \ln \left( \frac{\lambda_i}{\Lambda}
\right) \nonumber \\
& = & \sum^N_{j=1} \ln \tilde{p} (C_j)
\end{eqnarray}
where $C_j$ is counter in which $j$'th event arrived and $\tilde{p}(k)
= \frac{\lambda_k}{\Lambda}$ is relative probability of landing in
$k$'th counter.

\item Note $\tilde{p}$ is normalized ${\displaystyle\sum^M_{k=1}}
\tilde{p} (k) = 1$.

\item This is the discrete maximum likelihood method:  

\begin{description}
\item{$\bullet$} we have $N$ observations: 
\item{$\bullet$} each has only $M$ possible outcomes 
\end{description}

\item and the $L = {\displaystyle\prod^N_{j=1}} \tilde{p} (C_j)$ is
product of probabilities---normalized properly.
\end{itemize}
\end{slide}

