FRM Part I · FRM Exam Part I · Multivariate Random Variables
X and Y are random variables with Var(X) = 4, Var(Y) = 9 and Cov(X,Y) = -3. What is Var(2X - Y)?
Var(2X - Y) equals 37. It is 4×4 + 9 + 2×(2)(-1)×(-3) = 16 + 9 + 12. The negative covariance combined with opposite-sign weights adds to the variance rather than reducing it.
- A13
- B28
- C25
- D37Correct
Explanation
Var(2X - Y) = 4×4 + 1×9 + 2×(2)(-1)×(-3) = 16 + 9 + 12 = 37. Using a plus sign on the covariance term would give 13, which is wrong because the weights have opposite signs and the covariance is negative.
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