Covariance and Independence

Classical Mechanics Level 1

The covariance of two random variables X X and Y Y is equal to 4. Are X X and Y Y independent?

No Yes Maybe

Matt DeCross by Matt DeCross , 27, USA

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2 solutions

Dana Gracia
Mar 20, 2018

Cov (X,Y) is different than 0

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Matt DeCross
Apr 20, 2016

If X X and Y Y are independent, their joint PDF factorizes and E ( X Y ) = E ( X ) E ( Y ) E(XY) = E(X) E(Y) . This implies that Cov ( X , Y ) = 0 \text{Cov} (X,Y) = 0 if X X and Y Y are independent, which is not the case here.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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