# Expected wait time before departure

Heathrow Express departs every 15 minutes. Assuming no bias when passenger arrives at the station, how much he should expect to wait before Heathrow Express begins its brief and expensive journey?

Also, what is the right question: is it mean time before departure, median?

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Every time between $0$ and $15$ minutes is equally likely, so the mean and median are both $7.5$. –  Qiaochu Yuan Dec 9 '11 at 19:57