FRM Part I · FRM Exam Part I · Multivariate Random Variables
Random variable A has variance 9 and random variable B has variance 16. Their correlation is -0.5. What is the variance of the random variable 2A - B?
The variance is 76, not any listed figure; this item is flawed.
- A16
- B28
- C52Correct
- D40
Explanation
Cov(A,B) = -0.5 × 3 × 4 = -6. Var(2A - B) = 4×9 + 1×16 - 2×2×1×Cov = 36 + 16 - 4×(-6) = 52 + 24 = 76? Recompute: the cross term is 2·(2)(-1)·Cov = -4×(-6) = +24, giving 36 + 16 + 24 = 76.
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