Editing Pearson correlation coefficient (section)

===Pearson correlation coefficient in quantum systems===
For two observables, <math>X</math> and <math>Y</math>, in a bipartite quantum system Pearson correlation coefficient is defined as <ref>{{cite journal |first=M. D. |last=Reid |date=1 July 1989 |title=Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification |journal=Physical Review A |volume=40 |issue=2 |pages=913–923 |doi=10.1103/PhysRevA.40.913 |url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.40.913}}</ref><ref>{{cite journal |author1=Maccone, L. |author2= Dagmar, B. |author3= Macchiavello, C. |date=1 April 2015 |title=Complementarity and Correlations |journal=Physical Review Letters |volume=114 |issue=13 |pages=130401 |doi= 10.1103/PhysRevLett.114.130401 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.130401|arxiv=1408.6851 }}</ref>

:<math>\mathbb{Cor}(X,Y) = \frac{\mathbb{E}[X \otimes Y] - \mathbb{E}[X] \cdot \mathbb{E}[Y]}{\sqrt{\mathbb{V}[X] \cdot \mathbb{V}[Y]}} \,,</math>

where
*<math> \mathbb{E}[X] </math> is the expectation value of the observable <math> X </math>,
*<math> \mathbb{E}[Y] </math> is the expectation value of the observable <math> Y </math>,
*<math> \mathbb{E}[X \otimes Y] </math> is the expectation value of the observable <math> X \otimes Y </math>,
*<math> \mathbb{V}[X] </math> is the variance of the observable <math> X </math>, and
*<math> \mathbb{V}[Y] </math> is the variance of the observable <math> Y </math>.

<math>\mathbb{Cor}(X,Y)</math> is symmetric, i.e., <math>\mathbb{Cor}(X,Y)= \mathbb{Cor}(Y, X)</math>, and its absolute value is invariant under affine transformations.