00:00 Introduction 00:56 What is the inspection paradox? 02:01 A simple example 04:31 Strong version of the inspection paradox 04:58 Example 2 - strong version 10:31 Size bias explained
I love this. The last distribution is not a bad model for the trains in my city (where there are frequent problems). If I see the platform empty, I know I just missed a train but at least the trains are running!
To play off the students example: if you sample every time that is just a couple seconds after each minute mark, you get 10 1-minute waits, 10 2-minute waits... 10 5-minute waits, 9 10-minute waits, and another 8 waits that are longer than that. Averaging them all gives a wait time of 14.8 minutes, which I find to be slightly more paradoxical than the fact that a totally random distribution expects a slightly shorter wait time than this
the paradox can be made compatible with intuition if you just push the 50 minute bus scenario to an extreme :) imagine a bus schedule where a thousand buses arrive one microsecond after the other, and the 1001st bus arrives one whole second after the 1000th bus. now we have on average one bus every millisecond but an inspector can expect to have to wait around half a second to see a bus obviously pushing it with the bus schedule example but the principle is the same
so if i understand it the right way it all depends on the variance of time between busses arriving, doesnt it? If there was no variance, the t/2 statement should be true, the higher the variance gets to more inacurate the intuition gets, right?
Funny, I don't find this counterintuitive at all! The "just missed the bus" scenario will land you on the 50 minute bus happen only one out of ten times, where as showing up randomly will land you there half the time.
