Student Probability Seminar

The Inspection Paradox

Speaker: Terrence Alsup

Location: Warren Weaver Hall 805

Date: Thursday, April 19, 2018, 11 a.m.


Suppose buses arrive on average every 10 minutes according to a renewal process N(t). If you show up to the bus stop at some time T, then what is the amount of time you should expect to wait until the next bus? You might expect to wait half the length of the average interval, so 5 minutes, but you will actually end up waiting longer on average. This counter-intuitve result is known as the inspection paradox. In short, you are more likely to show up during a longer interval, so these longer intervals are over-sampled. We will prove this for a general inter-arrival distribution and give an explicit calculation for the case where N(t) is a Poisson process. We will also study the limiting behavior when t\to \infty. Finally, we discuss several practical implications of this paradox.