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Does zero correlation mean independence?

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Physics & Mathematics Expert for JEE Mains,Advanced & IMO,InMO with 9 yrs experience

NO, Correlation is a measure of LINEAR dependence . it is possible for two random variables to be uncorrelated but NON-LINEARLY dependent. for example V and I are linearly dependent (OHM's law) and correlated. but dispalcement and time are non-linearly dependent in accelerated motion s=ut+1/2at2 i...
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NO, Correlation is a measure of LINEAR dependence . it is possible for two random variables to be uncorrelated but NON-LINEARLY dependent.  for example V and I are linearly dependent (OHM's law) and correlated.

but dispalcement and time are non-linearly dependent in accelerated motion

s=ut+1/2at2

i have used an example that u must have studied in class ix physics which is nearly correct.

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Tutor

It means zero linear relationship.
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Teacher

Yes, if the correlation between two variable is zero then it means their values are independent of each other.
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It means two random variables have no linear dependency with each other.But they might have non-linear dependency.
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Tutor

I understand that if 2 random variables are independent, then their correlation is zero and I have seen many examples of this. However, I can't find any examples of when two random variables have zero correlation, yet are not independent.
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No , correlation means interdependence in the sense of statistics
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