FRM Part I · FRM Exam Part I · Multivariate Random Variables
X and Y are bivariate normal with means 0, standard deviations 2 and 3, and correlation 0.6. What is the conditional variance of Y given X = 1?
The conditional variance is 5.76. In a bivariate normal distribution, Var(Y|X) equals the variance of Y times one minus the squared correlation: 9 × (1 − 0.36) = 5.76. It is the same for every value of X, so X = 1 changes only the conditional mean.
- A5.76Correct
- B9.00
- C3.24
- D5.40
Explanation
For bivariate normal, Var(Y|X) = σY²(1−ρ²) = 9(1−0.36) = 9 × 0.64 = 5.76. It does not depend on the observed X. Option B ignores conditioning; option C uses 9×0.36, the explained part, which is the wrong piece.
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