Alex and Yan agree to meet at library between 5 pm and 5:30 pm to study. They will arrive independently. Let's call X the time after 5 pm when Alex arrives, and Y time after 5 pm when Yan arrives. X is distributed uniformly over interval [0,30] min, and so is Y.
(a) Determine joint density and cumulative probability distributions of X and Y.
(b) Calculate the probability that Alex and Yan both arrive in the first 10 min.
(c) Calculate the probability that Alex must wait for Yan for at least 5 minutes.
(d) Calculate the probability that their combined arrival time does not exceed 10 minutes.