IAI Actuarial Core Principles · Actuarial Statistics · Generating functions
A random variable X has moment generating function M(t) = (0.7 + 0.3e^t)^10. What is the variance of X?
The variance is 2.1. The MGF (0.7 + 0.3e^t)^10 identifies a Binomial distribution with n = 10 and p = 0.3, so the variance is npq = 10 × 0.3 × 0.7 = 2.1.
- A2.1Correct
- B3.0
- C0.21
- D2.52
- 21.0
Explanation
M(t) is the MGF of a Binomial(10, 0.3) variable. Variance = npq = 10 × 0.3 × 0.7 = 2.1. The value 3.0 is the mean, not the variance.
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