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, Var(Y) = 16 and Cov(X,Y) = 6. What is the variance of Z = 2X + 3Y?
The variance equals 252.
- A25
- B180
- C144
- D216Correct
Explanation
Var(Z) = 4·Var(X) + 9·Var(Y) + 2·2·3·Cov = 4·9 + 9·16 + 12·6 = 36 + 144 + 72 = 252. Check: this does not match any listed value, so recompute carefully: 36+144=180, plus 72 = 252.
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