FRM Part I · FRM Exam Part I · Multivariate Random Variables
Random variables X and Y have E[X] = 4, E[Y] = 10, Var(X) = 9 and Var(Y) = 16. The correlation between X and Y is 0.5. What is the variance of Z = X + Y?
The variance of X + Y is 37. The covariance is 0.5 × 3 × 4 = 6, so the variance equals 9 + 16 + 2×6 = 37. Ignoring the covariance would give 25, which understates the risk of the sum.
- A25
- B37Correct
- C49
- D31
Explanation
Cov(X,Y) = 0.5 × 3 × 4 = 6. Var(X+Y) = 9 + 16 + 2×6 = 37. Omitting the covariance term gives 25, which is wrong because the variables are correlated.
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