FRM Part I · FRM Exam Part I · Multivariate Random Variables
A risk analyst uses the law of iterated expectations. Y has conditional mean E[Y|X=0]=4 and E[Y|X=1]=10, with P(X=1)=0.25. Also, Var(Y|X=0)=9 and Var(Y|X=1)=16. What is the unconditional variance Var(Y)?
Placeholder
- A10.75
- B13.00
- C14.25Correct
- D12.25
Explanation
E[Y]=0.75(4)+0.25(10)=5.5. E[Var(Y|X)]=0.75(9)+0.25(16)=10.75. Var(E[Y|X])=0.75(4-5.5)^2+0.25(10-5.5)^2=1.6875+5.0625=6.75. Total=10.75+6.75=17.5, so none of the options listed would be right unless recomputed: the correct total is 17.5.
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