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

Learning about probabilistic inference and forecasting by playing with multivariate normal distributions