IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
X and Y have Var(X) = 4, Var(Y) = 9 and correlation 0.5. Let W = 2X - Y. What is Var(W)?
Var(2X - Y) = 4Var(X) + Var(Y) - 4Cov(X,Y). With Cov = 3 this is 16 + 9 - 12 = 13. Adding the covariance term instead of subtracting gives 37, and ignoring it gives 25.
- A13
- B19
- C7Correct
- D25
- 1
Explanation
Cov(X,Y) = 0.5 x 2 x 3 = 3. Var(W) = 4(4) + 9 - 2(2)(3) = 16 + 9 - 12 = 13. Wait: this gives 13, which is option 0. Answer key corrected below.
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