Find the expected value.
-A bus arrives at a bus stop at 10 am, 10 minutes past ten, and 11.00 am. You arrive at the bus stop at random times between 10.00 am and 11.00 am every day, so all arrival times are equally likely.
Find your expected waiting time for the bus.
[Hint: Find the probability that you will arrive at the bus stop between 10.00 am and 10 minutes
Past ten and find your mean waiting time in that case. Then find the probability that you will arrive
At the bus stop between 10 minutes past ten and 11.00 am and find your mean waiting time in that
Case.]

Question

Quizplus · Accepted Answer

The expected waiting time can be calculated by considering the two intervals separately: 10:00-10:10 and 10:10-11:00. For the first interval (10:00-10:10), the probability of arriving in this interval is 10/60 = 1/6, since the total interval from 10:00 to 11:00 is 60 minutes. If you arrive in this interval, your expected waiting time is 5 minutes (since the bus arrives at 10:10, and this is the midpoint of the interval 10:00-10:10).For the second interval (10:10-11:00), the probability of arriving in this interval is 50/60 = 5/6. The expected waiting time if you arrive in this interval is the average of the waiting times at 10:10 (0 minutes) and at 11:00 (50 minutes), which is 25 minutes.Therefore, the overall expected waiting time is:(1/6)*5 + (5/6)*25 = 5/6 + 125/6 = 130/6 = 21.7 minutes.

Find the Expected Value