re: Memorylessness at the Bus Stop: Using R on transit data to test a hypothesis VIEW POST


Doesn't this assume that the expected time never actually reaches zero? The far right hand side of the "exponential" graph is for night/holidays/whatever where the time between busses will be much longer than "normal", but it isn't infinite and there isn't a tiny chance that if you wait for a week you still won't see a bus.

This is obviously much easier to reason about in common situations where you know the bus is scheduled to arrive every 10 minutes, and you've waited 9, the chance you'll see one within 2 minutes is obviously much higher now than it was when you arrived.


Yes the exponential graph never touches zero, which seems impossible but makes more sense if you start to imagine the extremely improbable events that might cause a bus to take a week to arrive.

A grim example: if New York City is bombed, it might take a long time for the transit system to get back up and running, in which case waiting a week for a bus is conceivable. That's very unlikely, but that's also the point--the distribution is near zero for this length wait.

So even though nothing like that has happened (and hopefully never will), the idea could still be captured in the exponential distribution.

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