IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
Given q_40 = 0.02 and a uniform distribution of deaths (UDD) between integer ages, what is the force of mortality at exact age 40.5, to 4 decimal places?
Under UDD the force of mortality at age x+s is q/(1 - s·q). With q = 0.02 and s = 0.5 this is 0.02/0.99, which is about 0.0202. The force rises through the year even though deaths are uniform.
- A0.0200
- B0.0202Correct
- C0.0204
- D0.0198
- 0.0206
Explanation
Under UDD, μ(40+s) = q/(1 - s·q). With s = 0.5: 0.02/(1 - 0.01) = 0.02/0.99 = 0.020202, i.e. 0.0202. Option 0.0200 wrongly takes the force as constant at q.
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