Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 90 minutes without delay. What is the expected value of your waiting time?

Since you arrive randomly and all arrival times are equally likely, half the time you will arrive at the bus stop during the 90/2=45 minute period after the last bus left, and half the time you'll arrive during the 15 minute period before the next bus arrives.

In general, you'll arrive at the bus stop n < 45 minutes AFTER the last bus left and as often as you'll arrive at the bus stop n < 45 minutes BEFORE the next bus comes The average of those times, if we calculate, will be 45.

Hence, your average waiting time can be 45 and this means the "expected" value of your waiting time.

Suppose that you arrive at a bus stop​ randomly, so all arrival times are equally likely. The bus arrives regularly every 90 minutes without delay. What is the expected value of your waiting​ time?

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Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 90 minutes without delay. What is the expected value of your waiting time?