Seonglae ChoNormalized Covariance, measures linear correlation
The correlation coefficient, Pearson product-moment correlation coefficient, PPMCC, Bivariate correlation, Pearson's r
Since variance is non-negative, correlation bounds to -1 to 1 ()
Correlation does not imply Casuality such as spurious correlation. 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.
Other Correlations
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related.
Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
https://en.wikipedia.org/wiki/Correlation
Pearson correlation coefficient
In statistics, the Pearson correlation coefficient ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1.
https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
