If the covariance of two variables is 0, are they

dannyhaden6gjj

dannyhaden6gjj

Answered question

2022-02-12

If the covariance of two variables is 0, are they necessarily independent?

Answer & Explanation

lofia1r

lofia1r

Beginner2022-02-13Added 15 answers

No, if X and Y have pairs of values say:
(- 3, 9),(- 2 ,4), (- 1, 1) , ( 0, 0), (1, 1), (2, 4),(3, 9) their covariance is zero. But they are not independent, but related; as Y=X2
Explanation:
Cov(X,Y)=1nxyxy
=(17)×00×4=0 as
xy=3×9+(2)×4+(1)×1+0×0+1×1+2×4+3×9=2781+0+1+8+27=0.
Similarly x=0x=0

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