uses arrive to your local bus stop at fixed times, three buses per hour. You arrive to
Question:
uses arrive to your local bus stop at fixed times, three buses per hour. You arrive to the bus stop at X minutes after 9 o’clock, where X has continuous uniform distribution over the open interval ]0, 60[ (which does not include the endpoints).
(a) If the buses arrive regularly at 20-minute intervals, what is your expected waiting time for the next bus?
(b) Now from the timetable you learn that the buses arrive at 9:00, 9:10, 9:30, 10:00, . . . and so on. Represent your waiting time W for the next bus as a function W = g(X) of your arrival time, and draw a graph of the function. (Hint: define the function by breaking into cases.)
(c) Calculate E(W). Hint: Transformation formula.
(d) Compare results from (a) and (c), and explain with common sense
Managing Controlling and Improving Quality
ISBN: 978-0471697916
1st edition
Authors: Douglas C. Montgomery, Cheryl L. Jennings, Michele E. Pfund