The CABS buses travel with exactly 15 min headways on your route, including the fact that they service passengers at your bus stop for exactly 30 sec.
a) You arrive at your bus stop at some random point in the cycle, what is your expected wait time, w(t), to board a bus? Be sure to show your work or you will lose points.
(To keep the problem simple: [1] assume your time waiting for other passengers to board and alight is 0. [2] Do NOT count any time YOU spend on the bus after boarding but before the bus departs in w(t))
b) What is the standard deviation in w(t) given the fact that there is no bus waiting at your stop upon your arrival?