juniorProbability
What is covariance and what does it measure?
Updated May 17, 2026
Short answer
Covariance measures how two variables change together.
Deep explanation
Covariance = E[(X-μX)(Y-μY)] indicates direction of relationship. Positive covariance means variables increase together; negative means inverse relationship. It does not measure strength in standardized form.
Real-world example
Relationship between temperature and electricity consumption.
Common mistakes
- Interpreting covariance magnitude without scale normalization.
Follow-up questions
- What is difference between covariance and correlation?
- Can covariance be zero but dependent?