You are traveling from San Francisco to Casper Wyoming with

You are traveling from San Francisco to Casper, Wyoming, with a change of planes in Denver.

Your arrival time in Denver is uniformly distributed between 12:00 noon and 1:00 PM. Your con-

necting ight leaves Denver between 12:30 and 1:30 PM and the departure time is also uniformly

distributed and independent of the arrival time.

(c) What is the average amount of time you must wait in Denver? (Waiting does not include the

20 minutes needed to make the connection and, if you miss the ight, assume your waiting

time is zero.)

Solution

(c) What is the average amount of time you must wait in Denver?

Your arrival time in Denver is uniformly distributed between 12:00 noon and 1:00 PM. Your connecting flight leaves Denver between 12:30 and 1:30 PM .Wait time can be anything between 0 and 20m and each time in this range is as likely as any other time. Therefore, distribution of the wait time is U(0, <20 minutes).