Alice and Bob agree to meet at the dining hall for supper. Unfortunately, neither of them is very organized or very patient. Suppose that the random variables X = the time Alice arrives at the dining hall, and Y = the time Bob arrives at the dining hall are independent uniform random variables on the interval [5, 6]. (The units are hours after noon.)
a) What is the joint pdf for X and Y ?
b) What is the probability that both of them arrive before 5:30?
c) If neither of them is willing to wait more than 10 minutes for the other to show up, what is the probability that they eat together? That is, what is the probability that they arrive within 10 minutes of each other?