CorrelationMatrix
Fra mn/fys/epf
Revisjon per 25. mar. 2011 kl. 23:21 av Read@uio.no (diskusjon | bidrag)
The covariance matrix is
.
Suppose are three independent sources of normally-distributed unit fluctuations (with < δi > = 0 and < δi * δj > = δi'jand where δij is the kronikker delta function (1 for i = j and zero for ).
Pseudo-measurements of (x1,x2) can be generated from the expressions (x1,x2) = (x10 + α * δ1 + β * δ2,x20 + γ * δ3 + λ * δ2).
Expanding the covariance matrix one finds C12 = C21 = β * λ. Similar substitution for Ci'jgives for the diagonal matrix elementsabove and , one finds <x_1*x_2> = x_{10}*x_{20}+\beta*\lambda</math> so that
and
. so that C=
α2 + β2 β * λ