IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
Two independent lives each have a constant force of mortality: μ = 0.02 for (x) and μ = 0.03 for (y). What is the expected time until the first death, E[T_xy], to two decimal places in years?
The expected time to first death is 20.00 years. With independent constant forces, the joint-life force of mortality is 0.02 + 0.03 = 0.05, so T_xy is exponential with mean 1/0.05. Adding the individual means would be incorrect.
- A20.00Correct
- B33.33
- C50.00
- D83.33
- 12.00
Explanation
The joint-life force is the sum, 0.05, so T_xy is exponential with mean 1/0.05 = 20.00 years. Using 1/0.02 + 1/0.03 = 83.33 adds the individual means, which is wrong. Using 1/0.03 = 33.33 or 1/0.02 = 50 considers only one life.
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