  The properties of the normal distribution under linear transformation, as
well the easy way to compute the covariance matrix of marginals and
conditionals, offer a unique opportunity to get an insight about several
aspects of uncertainties in measurements. The way to build the overall
covariance matrix in a few, but conceptually relevant cases is illustrated:
several observations made with (possibly) different instruments measuring the
same quantity; effect of systematics (although limited to offset, in order to
stick to linear models) on the determination of the 'true value', as well in
the prediction of future observations; correlations which arise when different
quantities are measured with the same instrument affected by an offset
uncertainty; inferences and predictions based on averages; inference about
constrained values; fits under some assumptions (linear models with known
standard deviations). Many numerical examples are provided, exploiting the
ability of the R language to handle large matrices and to produce high quality
plots. Some of the results are framed in the general problem of 'propagation of
evidence', crucial in analyzing graphical models of knowledge.
