IAI Actuarial Core Principles · Actuarial Statistics · Expectations and conditional expectations
X is uniformly distributed on (0, 6). What is E[X²]?
E[X²] is 12. For a uniform distribution on (0, 6) the variance is 36/12 = 3 and the mean is 3, so E[X²] = 3 + 3² = 12.
- A3
- B9
- C12Correct
- D36
- 6
Explanation
E[X²] = ∫0^6 x²/6 dx = 6³/(3×6) = 216/18 = 12. Check: Var = 36/12 = 3, mean 3, so E[X²] = 3 + 9 = 12. Option 3 is only the variance, and 9 is the squared mean.
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