FRM Part I · FRM Exam Part I · Random Variables
Random variables X and Y have Var(X) = 9, Var(Y) = 16 and a correlation of 0.25. What is Var(2X − Y)?
Var(2X − Y) is 40. The covariance is 0.25 × 3 × 4 = 3, so the variance is 4×9 + 16 − 2×2×3 = 36 + 16 − 12 = 40. The covariance term is subtracted because Y enters with a negative coefficient.
- A40Correct
- B52
- C64
- D13
Explanation
Cov(X,Y) = 0.25 × 3 × 4 = 3. Var(2X − Y) = 4(9) + 16 − 2(2)(3) = 36 + 16 − 12 = 40. Ignoring covariance gives 52, and adding the covariance term instead of subtracting it gives 64.
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