IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
For an investigation using the exact age method with a constant force of mortality over the age interval, the total deaths are 45 and the central exposed to risk is 1,500 life-years. What is the approximate variance of the maximum likelihood estimator, evaluated at the estimate?
The MLE is 0.03 and its approximate variance is the estimate divided by exposure, 0.03/1,500, which equals 0.00002. Equivalently, deaths divided by exposure squared gives 45/2,250,000 = 0.00002, so the correct option is 0.000020.
- A0.000020
- B0.000600
- C0.000030Correct
- D0.030000
- 0.000300
Explanation
The estimate is 45/1,500 = 0.03. Var is approximately mu/E = 0.03/1,500 = 0.00002, or equivalently d/E^2 = 45/2,250,000 = 0.00002. Check the options: 0.000020 is that value.
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