CA Foundation · Quantitative Aptitude · Correlation and Regression
Two variables X and Y have standard deviations 3 and 4 respectively, and the correlation coefficient between them is 0.5. What is the variance of (X − Y)?
The variance of X − Y is 13. It equals 9 + 16 − 2 × 0.5 × 3 × 4 = 25 − 12. The covariance term is subtracted for a difference of variables. Adding it would give 37, which applies to X + Y.
- A13Correct
- B37
- C25
- D1
Explanation
Var(X − Y) = σx² + σy² − 2rσxσy = 9 + 16 − 2(0.5)(3)(4) = 25 − 12 = 13. The value 37 comes from adding the covariance term instead of subtracting it, which is the sign error. The value 25 ignores the covariance term altogether.
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