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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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Why is E[Cov(Y|X)]=Cov(Y|X) true in this case?

I'm given this equality when $X=Y+Z$ and $Y,Z$ are independent standard Gaussians. Why is this equality true?
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