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FRM 2000 Q 81

 the answer is b ...
2009 handbook p 40

which one is false?
b ) corelation  coefficient of zero means two random variables are independent.

why independence imply zero corelation,but the reserve is not always true??

回复:(ericlo321)FRM 2000 Q 81

举个反例试试

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When the correlation b/w A and B is 0, they are uncorrelated, but not necessarily independent in between. This is because the correlation coefficient detects ONLY LINEAR dependencies, i.e. correlations.

 

As an example, imagine X being constant of 3 and Y = X^2 for any given X. Clearly, Y is correlated to X. However, as there is NOT ANY linearity b/w the two variables, their CC = 0.

 

Hope this have been clear to you. 

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