The average wait for the ferry

Question

A ferry departs exactly every 30 minutes. You arrive at a uniformly random time. What is your expected waiting time, in minutes, for the next ferry?

Accepted Answer

Your wait is uniform on [0, 30] minutes. The mean of a uniform distribution on [0, T] is its midpoint: E[	ext{wait}] = \frac{0 + 30}{2} = 15 	ext{ minutes} . Takeaway. With evenly spaced service every T and a random arrival, the average wait is half the gap, 	frac{T}{2}, regardless of how long the cycle is.

The average wait for the ferry

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