Bus Route "A", with headways of 10 minutes, and Bus Route "B", with headways of 20 minutes, merge along a common route with the headway sequence of 5 min, 5 min, 10 min, 5 min, 5 min, 10 min, ... A passenger who wishes to travel along the common route (i.e., she's willing to take a bus from either route "A" or "B") arrives at a random time.

Determine:

a) the probability that the passenger must wait less than a time W for the next arriving bus (i.e., define and sketch the CDF for waiting time);

b) the probability that the passenger waits between 4 to 7 minutes for the next bus;

c) the passenger's expected waiting time;

and d) the probability that the first bus to arrive is from Route "B."