# Pdf/cdf Probability

You and your friend are trying to meet for lunch and both will arrive, independently of each other, uniformly and at random between 12 and 1pm. Let A and B be the number of minutes after noon at which you and your friend arrive, respectively. Then A and B are independent uniformly distributed random variables on [0, 60]. Hint: For parts (c-e) you might find it easiest to find the fraction of the square [0, 60]×[0, 60] filled by the event.

a)Find the pdf f(a, b) and the cdf F(a, b)

b)Find the probability that you will arrive before 12:30

c)Find the probability that you arrive before 12:15 and your friend arrives between 12:30 and 12:45 with two ways:

i)By using the fact that A and B are independent
ii)By shading the corresponding area of the square [0, 60] × [0, 60] and showing that the proportionof shaded area equals the probability.

d)Find the probability that you will arrive less than five minutes after your friend.

e)Now suppose that you and your friend are both impatient and will leave if you have to wait more than 15 minutes for the other to arrive. What is the probability that you and your friend will have lunch together?