IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A life aged 40 has future lifetime T_40 with constant force of mortality mu = 0.02 per year at all ages. What is the probability that this life dies between ages 45 and 50? Give the nearest value.
The probability is e^-0.1 minus e^-0.2, which is about 0.0861. With a constant force of 0.02, survival to 5 years is 0.9048 and to 10 years is 0.8187, and the difference is the chance of death between ages 45 and 50.
- A0.0861Correct
- B0.0950
- C0.1813
- D0.0905
- 0.0714
Explanation
Probability = 5p_5 ... precisely, P(5<T_40<=10) = e^{-0.02*5} - e^{-0.02*10} = e^{-0.1} - e^{-0.2} = 0.904837 - 0.818731 = 0.086106. Option 3 (0.0905) is e^{-0.1} approximately misapplied, and 0.1813 is the probability of death within 10 years.
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