Covariance

Probability · Formula · Appears in 1 lesson

Cov⁡(X,Y)=E ⁣[(X−E[X])(Y−E[Y])]\operatorname{Cov}(X, Y) = \mathbb{E}\!\left[(X - \mathbb{E}[X])(Y - \mathbb{E}[Y])\right]

Measures whether two variables rise and fall together. It is positive when they move in step, negative when they move oppositely, and zero when knowing one tells you nothing linear about the other.

Symbols

XX
The first random variable.
YY
The second random variable.
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