IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A survival model has μ(x) = 0.01 for all x (constant force, exponential lifetime). What is the median future lifetime of a life aged 30, to the nearest year?
With a constant force of 0.01 the future lifetime is exponential, so the median solves exp(-0.01m) = 0.5, giving m = ln2/0.01, about 69 years. The age of 30 is irrelevant because of the memoryless property, and the median is below the mean of 100.
- A50 years
- B100 years
- C69 yearsCorrect
- D63 years
- 74 years
Explanation
Median m satisfies exp(-0.01m) = 0.5, so m = ln 2/0.01 = 69.3 years, about 69. Age does not matter due to memorylessness. Option 50 years wrongly sets the median at half the mean life of 100.
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