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What is the formula to calculate conditional $\operatorname{Cov}(X, Y|X >1)$? I know how to calculate $\operatorname{Cov}(X, Y)$ but don't know how to calculate this one.

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You just condition the expectations on the given event: $\text{Cov}(X,Y|X>1)=\mathbb{E}[XY|X>1]-\mathbb{E}[X|X>1]\mathbb{E}[Y|X>1]$.

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