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A correlation statistic is not

zero if the two random variables are independent.

a normalized measure of the relationship between two random variables.

bounded between -1 and 1.

described by the formula $Corr(Y,X) = \frac{Cov(Y,X)}{Var(Y)\times Var(X)}$.

an indicator of the both the direction and strength of the co-movement between two random variables.