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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models

Under a constant force of mortality μ = 0.04 at all ages, what is the expected future lifetime E[T_x] and the median future lifetime respectively (ln 2 = 0.6931)?

The expected future lifetime is 25 years, being 1/0.04, and the median is 17.33 years, being ln2 divided by 0.04. The mean exceeds the median because the exponential distribution is right-skewed.

  1. A25.00 years and 25.00 years
  2. B25.00 years and 17.33 yearsCorrect
  3. C17.33 years and 25.00 years
  4. D25.00 years and 34.66 years
  5. 20.00 years and 17.33 years

Explanation

With constant force, T_x is exponential with mean 1/μ = 25. The median m solves e^{-0.04m} = 0.5, so m = ln2/0.04 = 17.33. The mean exceeds the median because the distribution is right-skewed, which rules out option A. Check: e^{-0.04×17.33} = e^{-0.6932} ≈ 0.5.

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