Correlation vs Dependance

There is no direct connection between correlation.

Correlation - Correlation only measures the linear association between the two random variable. Two dependant random variables might still have zero correlation if the association is not linear between them.

Independent variable - The notion of independant RV tells, if knowing about any of the one RV will tell any information about the other. Mathematically if X and Y are independent RV, then.

$$P(Y|X) = P(Y), P(X|Y) = P(X), P(X,Y) = P(X)P(Y)$$

Example of Dependent but uncorrelated variables

Why zero correlation does not necessarily imply independenceCross Validated

• If independent, then definitely uncorrelated

• If Dependent, then might correlated or uncorrelated

• If uncorrelated, may or may not be independent.

• If correlated, then definitely dependent.