Etymology:
The word "covariance" is derived from Latin:
Meaning:
In statistics, covariance is a measure of the joint variability of two random variables. It quantifies how much the two variables change together.
Origin:
The concept of covariance was first introduced by Francis Galton in his 1888 paper "Co-relations and their Measurement, Chiefly from Anthropometric Data". Galton used the term "co-variance" to describe the relationship between two variables that tend to vary together.
Explanation:
Covariance measures the extent to which two random variables, X and Y, move in the same or opposite directions. A positive covariance indicates that the variables tend to increase or decrease together. A negative covariance indicates that the variables tend to move in opposite directions.
The covariance between two random variables is defined as:
Cov(X, Y) = E[(X - μX)(Y - μY)]
where:
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