Independence vs uncorrelatedness — what's the difference?
mediumAnswer
- Independent means P(A, B) = P(A) P(B): no relationship at all.
- Uncorrelated means covariance = 0: no linear relationship.
- Independence implies uncorrelated, but the reverse is false in general — X and can have zero correlation while being fully dependent.
- For jointly Gaussian variables, uncorrelated implies independent — a special case.
Check yourself — multiple choice
- Uncorrelated implies independent in general
- Independent implies uncorrelated; the converse holds only for Gaussians
- They are always equivalent
- Covariance = 0 always means variables are unrelated
Independence is strictly stronger than uncorrelatedness in general.
#probability#variance
Practise Statistics Fundamentals
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