IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
A random variable X has E[X] = 4 and Var(X) = 9. Let Y = 3 − 2X. What is E[Y²]?
E[Y²] equals 61. Y has mean 3 − 2(4) = −5 and variance (−2)² × 9 = 36, so E[Y²] is the variance plus the squared mean: 36 + 25 = 61.
- A25
- B36
- C61Correct
- D1
- 37
Explanation
E[Y] = 3 − 8 = −5. Var(Y) = 4 × 9 = 36. E[Y²] = Var(Y) + (E[Y])² = 36 + 25 = 61. Choosing 25 forgets the variance term, and 36 forgets the squared mean.
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