A passenger arrives at a bus stop at 10 am knowing that bus will arrive at random time between 10 am and 10:30 am. What is the probability that he will have to wait lower than 10 minutes?If the bus has not arrived until 10 : 15 am, what is the probability that he will have to wait another 10 minutes?
Expert's answer
Solution:
Given that Bus arrives uniformly at the bus stop between 10 am and 10 :
30 am. Let X denote the arrival of the bus at the bus stop. Then, X is a uniform random variable having density as
(a): Probability that a passenger arriving at the bus stop between 10 and 10: 30 will have to wait less than 10 minutes.
(b): The bus hasn't arrived till 10: 15 am. The probability that the passenger will have to wait for an additional 10 minutes is given as
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