Today, we are brought the sad news that Europe's oldest woman died. A little over a week ago the oldest person in the U.S. unfortunately died. Yesterday, the Netherlands' oldest man died peacefully. The Gerontology Research Group keeps records: Guinness World Records.
If you live in a country with $N_{\text{country}}$ people, a continent with $N_{\text{continent}}$ people, and a world with $N_{\text{world}}$ people, during a year and on average, how often will you be notified (if you're paying attention to your quality tabloid) of the death of the oldest man/woman/person alive of your country/continent/world? (Note that a death will result in at most one notification.)
Edit, Suggestions (due to comments; thanks!) only:
Ultimately, I am looking for a realistic formula. That means that life tables are certainly allowed (but mind the ending, and note that some of the oldest people are older than the maximum in the tables).
I guess that the Gompertz–Makeham law of mortality, or any plausible model of late-life mortality, is also fair game.
However, these suggestions do not preclude some insight or realistic assumption that might not need any of those things.
Further potentially useful assumptions (with regard to a subpopulation) may include (if reasonable w.r.t. the question):
- Time is discrete.
- The number of births at any time is constant.
- The number of deaths at any time is constant.
- The number of births is equal to the number of deaths at any time.
- Time is defined in such a way that, at any time, one birth and one death occur.
- In the limit to infinite age, the probability of a person of such age dying goes to $1$.
- At any time, the oldest person(s) alive is (are) the most likely to die.
- At any time, an older person(s) alive is (are) more likely to die than any younger person alive.
(Although such assumptions aren't necessarily realistic, I don't immediately see how they would distort the outcome.)