IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
Under a two-state model with constant force of mortality μ, a life aged x is observed for the whole of a one-year period. Which expression gives the probability that death occurs in the second half of the year (between t = 0.5 and t = 1)?
The probability is e^(-0.5μ) minus e^(-μ): survival to the half-year point less survival to the end of the year. The other options describe death in the first half or in the following year.
- Ae^(-0.5μ) - e^(-μ)Correct
- B1 - e^(-0.5μ)
- C0.5μ e^(-μ)
- De^(-μ) - e^(-2μ)
- μ e^(-0.5μ)
Explanation
Probability of death in (0.5, 1) = P(survive to 0.5) - P(survive to 1) = e^(-0.5μ) - e^(-μ). Option 1 is the probability of dying in the first half. Option 3 would be the second year.
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