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

A lifetime has force of mortality μ(t) = 0.01t for t ≥ 0, with t in years. What is the probability that a new life dies between times 5 and 10?

The probability is exp(−0.125) − exp(−0.5). Integrating the force 0.01t gives cumulative hazard 0.005t², so S(5) = e^−0.125 and S(10) = e^−0.5, and the probability of death in the interval is their difference.

  1. Aexp(−0.125) − exp(−0.5)Correct
  2. Bexp(−0.25) − exp(−1)
  3. Cexp(−0.5) − exp(−0.125)
  4. Dexp(−1) − exp(−0.25)
  5. 0.375

Explanation

Cumulative hazard is 0.005t². S(5) = exp(−0.125) and S(10) = exp(−0.5). P(5<T≤10) = S(5) − S(10) = exp(−0.125) − exp(−0.5). Using 0.01t² instead of 0.005t² gives option 1, a forgotten factor of one half; the reversed difference is negative.

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