

\subsection{\bf Multiplication of Experiments}
\begin{slide}
\begin{itemize}
\item If we have two experiments that are independent but depend on
the same theoretical parameter $\alpha$.  Then
\begin{eqnarray*}
L_1 & = & \prod^{n_1}_{i=1} p (x_i, \alpha)\ \ \mbox{is likelihood of
experiment \# 1} \\
L_2 & = & \prod^{n_2}_{i=1} q (y_i, \alpha)\ \ \mbox{is likelihood of
experiment \# 2}
\end{eqnarray*}

\item and clearly the combined likelihood is
\[
L = L_1 L_2
\]

\item This final $L$ is correct expression of results of both
experiments.

\item i.e., one should {\bf multiply\/} likelihoods when combining
experiments.  

\item We will now apply this to case when each $L_i$ is Gaussian in
theoretical parameter $\alpha$.
\end{itemize}
\end{slide}

