FRM Part I · FRM Exam Part I · Random Variables
Independent random variables X and Y have Var(X)=9 and Var(Y)=16. What is Var(X - Y)?
Var(X−Y) is 25. With independence the covariance is zero, and the variance of a difference adds the two variances: 9+16. Subtracting them is wrong, and 5 is the standard deviation, not the variance.
- A-7
- B25Correct
- C7
- D5
Explanation
For independent variables covariance is zero, so Var(X-Y)=Var(X)+Var(Y)=9+16=25. Subtracting variances gives -7, which is impossible; 5 is the standard deviation.
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