# Student mortality

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 ${M(k,n)}$ be the number of former students of age ${k}$ after ${n}$ years. Then ${M(20,n)=170}$ and ${M(k+1,n+1)=M(k,n)(1-r_k)}$ for ${k\ge 20}$. It remains to sum ${M(k,n)}$ over ${k}$ and subtract the result from ${170\,n}$.