For the country of Bienna, you are given:
(i) Bienna publishes mortality rates in biennial form, that is, mortality rates are of the form:
(ii) Deaths are assumed to be uniformly distributed between ages [math]2 x[/math] and [math]2 x+2[/math], for [math]x=0,1,2, \ldots[/math]
(iii) [math]{ }_{2} q_{50}=0.02[/math]
(iv) [math]{ }_{2} q_{52}=0.04[/math]
Calculate the probability that (50) dies during the next 2.5 years.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: B
[math]{ }_{2.5} q_{50}={ }_{2} q_{50}+{ }_{2} p_{50}{ }_{0.5} q_{52}=0.02+(0.98)\left(\frac{0.5}{2}\right)(0.04)=0.0298[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.