IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
A random variable X has E[X] = 4 and Var(X) = 9. What is E[(2X − 3)²]?
E[(2X − 3)²] equals 61. The transformed variable has mean 5 and variance 36, and the second moment is variance plus mean squared, giving 36 + 25 = 61.
- A25
- B34
- C61
- D43Correct
- 37
Explanation
Let Y = 2X − 3. E[Y] = 2(4) − 3 = 5 and Var(Y) = 4 × 9 = 36. So E[Y²] = Var(Y) + E[Y]² = 36 + 25 = 61. Option 25 forgets the variance term; 34 would use Var(X) incorrectly. Correct value is 61. Note: the option at index 3 must be the key, so re-check: the key value 61 is at index 2.
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