Suppose that the inter-arrival time between consecutive buses is 15 minutes with probability 0.5 and 30 minutes with probability 0.5. You just arrived at a bus stop. What is your expected waiting time?
My attempt: my gut tells me (since no real information about the type of distribution is provided) that it should just be 22.5 by splitting them down the middle. Is this correct?
Best Answer
The expected waiting time = 11.25 minutes, in my opinion.
Expected time if the inter-arrival time is 15 minutes with probability 1 = 7.5 mins
Expected time if the inter-arrival time is 30 minutes with probability 1 = 15 mins
Now, expected waiting time = $0.5 * (7.5 + 15)=11.25$