Normalized Covariance, measures linear correlation
The correlation coefficient, Pearson product-moment correlation coefficient, PPMCC, Bivariate correlation, Pearson's r
Correlation does not imply causation such as spurious correlation.
Since variance is non-negative, correlation bounds to -1 to 1 ()
Uncorrelated This means that there is no linear relationship.
Difference with Convolution is flip
Uncorrelated does not imply independence. However, if two random variables X and Y are Normal distribution uncorrelated, then they are Pairwise Independence. Since zero correlation makes Covariance Matrix and thus inverse of covariance matrix become diagonal. The joint PDF simplifies to the product of two independent normal distributions which satisfies Pairwise Independence.
The correlation between an Even function and the original variable is zero. (Integral cancels out) Naturally, even powers also exhibit this property.
Correlations