You have the option of catching a train to work every day at either the L Street Station or the M Street Station. At either station, trains arrive on average every two minutes. That is, each station is served by an average of 30 trains per hour. The train line serving the L Street Station stops at the station every two minutes without fail. The train line serving the M Street station arrives more randomly: 80% of the time, only 1 minute separates the arrival of one train and the next, but 20% of the time there’s a 6-minute interval between the arrival of one train and the next. If your arrival time at the station is random, what is your expected waiting time at the
a. L Street Station?
b. M Street station?
c. Which station would you choose? Explain.
The Poisson and Exponential distributions are closely connected, as demonstrated in the next two exercises: