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# Does zero correlation mean independence?

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...

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.

Tutor

It means zero linear relationship.

Teacher

Yes, if the correlation between two variable is zero then it means their values are independent of each other.

It means two random variables have no linear dependency with each other.But they might have non-linear dependency.

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.

No , correlation means interdependence in the sense of statistics

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