probabuility distribution? "A train leaves a station on the hour & at a quarter of.")

probabuility distribution? "A train leaves a station on the hour & at a quarter of.")

A train leaves a station on the hour and at one quarter to the hour. Bob arrives at the station at a random time. How long can he expect to wait ?

The answer is "18 mins 45 seconds".

I know that a probability distribution is the way to go, getting started is the tricky bit. Are there a variety of methods that can be used? Thank you.

miamivince said:

A train leaves a station on the hour and a quarter to the hour. Bob arrives @ the station @ a random time. How long can he expect to wait ? The answer is 18 mins 45 seconds. I know that a probability distribution is the way to go, getting started is the trick bit. Is there a variety of methods that can be used ? Thanks.

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What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


Hint: First assume that the 'arrives at a random time' means the wait time is linear between zero min [arrives when the train is leaving] to either 45 min [arrives just as the train left on the hour] or between zero and 15 min [arrives just as the train left on the quarter to the hour]. If that is the case, what is the wait time function? Given the wait time function, what is its average?