If X and Y are any random variables with E(X)= 3, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the relationship between X and Y is a: $$\text { Hint: } \operatorname { corr } ( X , Y ) = \operatorname { Cov } ( X , Y ) / ( ( \sqrt { V ( X ) } \sqrt { V ( Y ) } ) = ( E ( X Y ) - E ( X ) E ( Y ) ) / ( \sqrt { V ( X ) } \sqrt { V ( Y ) } )$$

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The correlation coefficient is:$$\operatorname { corr } ( X , Y ) = ( 12 - 3 \cdot 2 ) / ( \sqrt { 16 } \sqrt { 25 } ) = 0.4$$Since the correlation coefficient is positive and less than 1, the relationship between X and Y is a weak positive relationship.

If X and Y Are Any Random Variables with E(X)=