Does both the Cov(x,y)= 0 and the Corr(x,y)= 0 for random variables x and y to be independent. Is it possible random variables are correlated whilst the covariance is zero?
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Is this self-study or for a course? Try searching for the definition of covariance. That should help. – dankernler May 08 '18 at 16:54
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If the covariance is 0 the correlation between the variables must also be 0 and vice versa.This question differs from the title. If the title is the actual question the answer is no. Their exist random variables that are uncorrelated and yet are not statistically independent. – Michael R. Chernick May 08 '18 at 17:05
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If the question is not like the title but like the text then it is not a duplicate, at least not in relation to the current referred previous question. – Sextus Empiricus May 08 '18 at 17:18
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No, it is not possible. In order to see this, note that
$Corr(x, y) = \frac{Cov(x, y)}{\sqrt{Var(x)}\sqrt{Var(y)}}$
Since $Cov(x, y)$ is zero, there is no way that the fraction can become positive/negative.

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