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Concerning two random variables

20 votes

What kind of distribution is this? $\text{Cov}(X, Y)=0$ but $\text{Corr}(X, Y)=1$

Since the covariance depends on the scale of $X$ and $Y$ and the correlation does not (rescaled to $[-1, -1]$) it is possible. For example, if the variance decreases towards zero: If $X=Y$ and $\sig …
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