Error propagation

If  is a set of random variables with the covariance matrix Cx, and if File:Hepa img275.gif , File:Hepa img276.gif is a set of transformed variables with transformation functions which are linear or well approximated by the linear terms of the Taylor series

File:Hepa img277.gif

in the neighbourhood of the mean E(X), then the covariance matrix Cy of File:Hepa img278.gif is

File:Hepa img279.gif

where T is the matrix of derivatives (  Jacobi Matrix)

File:Hepa img280.gif

If the Xi are independent, i.e. if Cx is diagonal, the variances of the Yi are given by the so-called law of law of error propagation

File:Hepa img281.gif

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