FRM Part I · FRM Exam Part I · Random Variables
Which statement about independence and correlation of two random variables is correct?
Independence implies zero covariance, provided the relevant moments exist, because the expected product then equals the product of expectations. The reverse is not generally true: zero correlation only rules out linear dependence and nonlinear dependence can remain.
- AZero correlation implies independence for any joint distribution
- BIndependence implies zero covariance, provided the moments existCorrect
- CNonzero covariance is compatible with independence
- DIndependence requires the correlation to equal one
Explanation
If X and Y are independent, E[XY]=E[X]E[Y], so covariance is zero. The converse fails in general, e.g. Y=X² with X symmetric about zero has zero covariance but is dependent.
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