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Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.

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Covariance definition

The variance formula is $Var(X,X) = E(X^2)-E(X)^2 =E(XX)-E(X)E(X)$ So the co-variance would be $Var(X,Y) = E(XY)-E(X)E(Y)$ $$ E(XY) - E(X)E(Y) \\ =E(XY) - E(X)E(Y) - E(X)E(Y)+E(X)E(Y) \\ =E(XY) - XE …
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