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I have two random variables $X$ and $Y$. Both are distributed according to $N(0,1)$. If their covariance is 0, are they independent?

I know that this is not true for other distributions, say the Wikipedia example: $X$ chosen uniformly in $[-1,1]$ and $Y=X^2$.

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up vote 4 down vote accepted

http://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent

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Thanks for the quick response. –  user915 Feb 10 '11 at 3:17

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