# Covariance

A measure of linear dependence

1. of a sample

Given a sample of $$n$$ pairs of values $$x_i, y_i$$ with means $$\mu_x$$ and $$\mu_y$$, the covariance is defined as
$\frac{1}{n}\sum_{i=1}^{n}\left(x_i - \mu_x\right) \times \left(y_i - \mu_y\right)$
where $$\sum$$ is the summation sign.

2. of a distribution

For a pair of random variables $$X$$ and $$Y$$ having a given joint distribution with means of $$\mu_X$$ and $$\mu_Y$$, the covariance is equal to the expectation of the function
$f(X, Y) = \left(X - \mu_X\right) \times \left(Y - \mu_Y\right)$

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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