Annie and Alvie have agreed to meet between
5:00 P.M. and 6:00 P.M. for dinner at a local
health-food restaurant. Let X =
Annie's arrival time and Y =
Alvie's arrival time.
Suppose X and Y are
independent with each uniformly distributed on the
interval [5, 6].
(a) What is the joint pdf
of X and Y?
f(x,y)
=
5 ≤ x ≤ 6,
5 ≤ y ≤ 6
otherwise
(b) What is the probability that they both arrive
between 5:30 and 5:45?
(c) If the first one to arrive will wait only 10 min
before leaving to eat elsewhere, what is the probability that they
have dinner at the health-food restaurant? [Hint: The
event of interest is A =
(x, y):
|x − y| ≤ 1/6
.] (Round your answer to three decimal places.)