Orthogonality and Correlation

Posted: August 16, 2014 in Educational Material
Tags: , , ,

I realized today that orthogonality and non-correlation (in the linear sense) of two random variables X and Y are strongly linked in our minds – and they shouldn’t. The fact is that whether orthogonality, i.e. E(XY)=0, implies correlation, or non-correlation, depends on whether the expected values of the variables are non-zero or not. I believe in the power of tables -so here it is, and easily verifiable from the definition Cov(X,Y) = E(XY) – E(X)E(Y)

 

Orthog Corrle table

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