The death of a former student brought to mind the question: what is the expected number of students that a professor will have outlived after N years of teaching? The obvious source of data is the CDC mortality table. However, a recent study found (perhaps unsurprisingly) that the mortality rate of U.S. college students is much lower than among the general U.S. population of same age. I don’t have access to the article itself, but the numbers quoted in the abstract add up to 19.44 deaths per 100,000. Compare this to the CDC rates for general population:
The rate jumps up at 21 so much that it stabilizes for two years afterwards.
I decided to use the 19.44 rate for ages up to 22, and switched to CDC rates afterwards. Unfortunately, CDC does not group results by educational level; presumably, college graduates would have a lower rate even after leaving the protective shell of their campus. To simplify the computation, I assumed the student age to be 20 at the time of taking my class. Over my first 8 years of full-time teaching I averaged 170 undergraduate students per academic year. Assuming the trend continues, I came up with the following prediction:
|Years of teaching||Deceased former students|
Also in the graph form:
The computation is straightforward: let be the number of former students of age after years. Then and for . It remains to sum over and subtract the result from .