

\subsection{\bf Errors in Linear Combinations}
\subsection{\bf of Uncorrelated Variables}

\begin{slide}
\begin{itemize}
\item In practice, when off diagonal terms are not given, one assumes
they are zero, i.e., variables are uncorrelated.  

\item This assumption/assertion gives:
\begin{equation}
\sigma^2_{y_i} = \sum^n_{j=1} \left( T_{ij}\right)^2 \sigma^2_{x_j}
\end{equation}
which is the usual rule of addition of errors in quadrature.  

\item One has to
emphasize that this ``usual'' rule is only valid where $x_j$ uncorrelated,
and usually $x_j$ are correlated!
\end{itemize}
\end{slide}

