plainglazed noted that the investigator measures the entire time interval between buses; k-man was first to hit on the crux of the correct analysis (getting the mark); and plasmid beautifully and comprehensively reminded me again that I used to know how to evaluate integrals. Uh, rephrase. Has reminded me that I no longer recall how to evaluate integrals ... without looking them up. Kudos to all. The idea is that
Here's the quick analysis provided by the Quora article I mentioned at the top:
The idea is similar to BMAD's puzzles about random arcs on a circle enclosing a particular point.
The arcs correspond to interval times and the point corresponds to the sampling process.E[T]=∑ttp(t)=10260+35260+10260+5260≈25