Covariance Probability Interview Questions
Covariance probability interview prep for dependence, expectation of products, indicator examples, and independence mistakes.
Candidates moving from probability basics into statistics-style quant interview prompts.
Covariance measures joint movement
Covariance describes whether two quantities tend to move above or below their means together. Positive covariance means same-direction movement is common; negative covariance means opposite-direction movement is common.
Use expectation of a product
A common form is E[XY] - E[X]E[Y]. The hard part in interviews is usually finding E[XY], which often requires understanding the joint distribution.
Concrete example
If X and Y are independent fair die rolls, E[XY] = E[X]E[Y], so covariance is 0. If Y is always equal to X, the covariance is positive because high X comes with high Y.
Independence connection
Independence implies zero covariance when expectations exist, but zero covariance does not always imply independence. State this direction carefully.
Indicator examples
For event indicators, covariance compares P(A and B) with P(A)P(B). This makes covariance another way to discuss dependence between events.
Common mistakes
Candidates often treat covariance, correlation, and independence as the same idea. Translate the question into joint behavior before choosing a formula.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.