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Math and science::INF ML AI
Covariance
Let \( (\Omega, \mathrm{F}, \mathbb{P}) \) be a discrete probability space let \( X: \Omega \to S_x \) and \( Y : \Omega \to S_y \), be two random variables, where \( S_x\) and \( S_y \) are finite subsets of \( \mathbb{R} \). Then the covariance of \( X \) and \( Y \) is defined as the
mean of the following random variable:
[\[ Z = \;\; ? \; \]]
In terms of \( X \) and \( Y \), the calculation for covariance is thus:
[\[ \mathrm{Cov}[X, Y] = \sum_{?} ? (? - \mathrm{E}[X])(? - \mathrm{E}[Y])) \]]
