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wubzwaters
20.07.2019 •
Mathematics
Suppose ancient romans had a 0.2 chance of dying in each of the following age intervals: [0, 2], [2, 10], [10, 30], [30, 70] and [70, 90]. to keep calculations straightforward, let's assume that, conditional on dying in any one of those five buckets, age at death was uniformly distributed across the interval. that means that, conditional on dying between age 0 and 2, the average roman lived to be 1 year old; conditional on dying between age 2 and 10, the average was 6 years; et cetera. under these (fictitious) numbers, life expectancy at birth was only 31.4 years, due largely to child mortality. what was the life expectancy (i.e. expected age at death) of an ancient roman who was still alive at age 30? it's much more than 31.4 years — can you figure out why?
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