Public Policy and Political Science
During the Cold War there were frequent radio tests of alert warnings. The regular program was interrupted and replaced by a long high-pitched signal. An announcer would break in with a message similar to, "This has been a test of the emergency broadcasting system.'' Suppose the time (in hours) between these tests had an exponential distribution with mean 24 hours.
a. If a test occurred at 6:00 a.m., what is the probability that another one would occur before 6:00 p.m.?
b. If a test occurred at 10:00 p.m., what is the probability that another one would not occur until after 6:00 a.m.?
c. If a test occurred at 9:00 a.m., what is the probability that the next test would occur between 12:00 p.m. and 1:00 p.m.?