Consider a 10 mile length of road with mile markers exactly every mile including 0 and 10. Starting at the 0 marker, you drive towards 10 and randomly stop at some point with a position "p" defined as (0 marker)<= p <=(10 marker).

Part 1 (teaser): - What is the expected value of the distance from "p" to the nearest mile marker?

Part 2 (more difficult): - Three mile markers, randomly selected, have been removed by vandals, but 0 and 10 remain. Same question as part 1.

Part 3: - Consider part 2, but markers 0 and 10 are also potentially part of the vandalism.
Does the answer change from part 2, and if so what is it?
(You have no problem knowing where to start your trip, even if marker 0 happens to be missing)

the distance from "p" to the nearest mile marker is between 0 and 1/2, and each value is equally likely. Therefore the expected value is 1/4

Posted by chun on 2017-08-30 09:54:36