Taxis depart the railway station to the airport from the early morning till late at night. Taxis leave the railway station with independent interdeparture times that are exponentially distributed with an expected value of 20 minutes. Suppose you plan to arrive at the station at 3 pm. What is the expected value and standard deviation of you waiting time?

Attempt:

Let X be your waiting time. I know that lambda = n * p. But how do you get lambda here? After I get lambda, I'm going to use the density function times x to get the expected value. But what do I integrate over? 0 to infinity?

Thanks.