Question

Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 30 minutes without delay (say, on the hour and on the half hour). What is the expected value of your waiting time? Explain how you got your answer.

Answer 1

E(x) = 15 minutes

Explanation:

The random variable X (waiting time) has a uniform distribution between the interval [0,30], because it is just as likely that you arrive in any time and then your waiting time is minimum 0 minutes and maximum 30 minutes

The expected value of a random variable uniform is:

E(x) =
`(a+b)/(2)`

Where a and b are the interval's extremes

Thus

E(x) =
`(0+30)/(2)`

E(x) = 15 minutes