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

For a life aged 50 with future lifetime T_50, the median future lifetime is defined as the value m satisfying which condition?

The median future lifetime m satisfies S_50(m) = 0.5, meaning there is a 50% chance of surviving beyond m. It is a quantile of the lifetime distribution and generally differs from the mean expectation of life.

  1. AThe force of mortality at age 50+m equals 0.5
  2. BS_50(m) = 0.5Correct
  3. CThe integral of S_50(t) from 0 to m equals 0.5
  4. Dm equals E[T_50]
  5. f_50(m) = 0.5

Explanation

The median is the time by which exactly half of the cohort has died, so P(T_50 > m) = S_50(m) = 0.5. It generally differs from the mean e°_50 unless the distribution is symmetric.

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