ATLAS hints
Fra mn/fys/epf
Revisjon per 6. mai 2011 kl. 17:31 av Read@uio.no (diskusjon | bidrag) (→Mean or average of two partially correlated measurements)
The derivation of the terms in the correlation matrix
The covariance matrix is
.
Suppose are three independent sources of normally-distributed unit fluctuations (with < δi > = 0 and < δi * δj > = δij
and where is the kroneker delta function (1 for 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
Using the properties of C12 = C21 = β * λ. Similar substitution gives for the diagonal matrix elements
and
so that
C=
α2 + β2 | β * λ |