IAI Actuarial Core Principles · Actuarial Statistics · Generating functions
X has MGF M(t) = (1 − 2t)^-3 for t < 0.5. What is the mean of X?
The mean is 6. Differentiating the MGF gives M'(0) = 3 × 2 = 6, matching a Gamma distribution with shape 3 and scale 2.
- A3
- B12
- C2
- D1.5
- 6Correct
Explanation
M'(t) = 6(1 − 2t)^-4, so M'(0) = 6. This is a Gamma with shape 3 and scale 2, mean 3 × 2 = 6. The value 3 ignores the scale.
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