IAI Actuarial Core Principles · Actuarial Statistics · Generating functions
The moment generating function of a random variable X is M(t) = (0.3 + 0.7e^t)^10. What is Var(X)?
The MGF matches a Binomial distribution with n = 10 and p = 0.7. Its variance is npq = 10 × 0.7 × 0.3 = 2.1. The figure 7.0 is the mean, not the variance.
- A2.1Correct
- B7.0
- C4.9
- D0.21
- 21.0
Explanation
The MGF is that of a Binomial(10, 0.7). Var = npq = 10 × 0.7 × 0.3 = 2.1. The value 7.0 is the mean, and 4.9 results from using n·p² instead of npq.
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