Problem bank
Problem 189 of 333MediumProbabilityP189
The bus waiting-time paradox
Buses arrive at a stop as a Poisson process with rate 4 per hour, so the average gap between buses is 15 minutes. You arrive at a uniformly random time, long after service started.
(a) What is your expected wait for the next bus?
(b) What is the expected time since the previous bus left?
(c) What is the expected length of the gap between buses that contains your arrival? Why is it not 15 minutes?
(d) Compare with buses that run exactly every 15 minutes.
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