Question

Berry arrives at a train stop at 7:00AM. If a train arrives at a random time between 7:16AM and 7:31AM, then find Berry's expected waiting time in minutes.

Answer 1

Berry arrives at a train stop at 7.00AM.

A train arrives at a random time between 7:16AM and 7:31AM, so if X denotes the time (in minutes) when the train arrives Then, X~uniform(0,15).

Since the Berry arrives at the train stop at 7.00 AM he already has to wait for at least 16 minutes. Then let Y denote the time(in minutes) that Berry has to wait for. Y= 16+X

The, expected waiting time in minutes= E(Y)= E(16+X)= 16+ E(X)

E(Y)=16+7.5= 23.5

So, it is expected that he will have to wait for 23.5 minutes, for the train to arrive.