On an exercise sheet I found the following question:
You monitor planes landing at an international airport. X measures the time intervals between consecutive landings. Is X exponentially distributed (in good approximation)?
To me it seemed that this is a clear case of an exponential distribution. However, the correct answer, supposedly, is no.
Can you explain to me why X is not exponentially distributed?
It slightly depends on how busy the airport is, but note
(a) the mode of an exponential distribution is $0$ while (ignoring emergencies) there is usually a substantial gap between planes landing so the first can clear the runway, and
(b) in a busy airport with restricted landing slots the controllers try to make planes tend to land with close to equal gaps between them to balance efficiency and safety, so a low standard deviation of gaps compared to their average, while an exponential distribution has a standard deviation equal to its average