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:

Age | Mortality rate |
---|---|

18 | 64.4 |

19 | 71.1 |

20 | 76.5 |

21 | 87.2 |

22 | 86.8 |

23 | 88.4 |

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 |
---|---|

8 | 2 |

10 | 4 |

15 | 12 |

20 | 25 |

25 | 45 |

30 | 74 |

35 | 120 |

40 | 188 |

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 .