IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
Y = 3 - 2X, where X has variance 5. What is Cov(X, Y)?
Cov(X,Y) is -10. Covariance ignores the added constant 3 and scales by the coefficient -2, giving -2 times Var(X) = -2 x 5. The negative sign reflects the decreasing linear relationship.
- A-10Correct
- B-2
- C10
- D-7
- 3
Explanation
Cov(X, 3 - 2X) = -2 Var(X) = -2 x 5 = -10. The constant 3 does not affect covariance. Choosing -2 forgets to multiply by the variance.
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