Jill arrives at a restaurant at 6PM and waits for her three friends Moe, Agnes, and Dorothy. Each one of her friends arrives independently at a time uniformly distributed between 6PM and 7PM. (a) Find the expected value of the time at which Moe arrives. (b) Find the PDF of the time T at which ALL three friends have arrived. (Hint: find the CDF of T and use independence of the arrivals). (c) Find the probability that Jill has to wait more than half an hour by herself. (d) Find the PDF of T given that Moe arrives at 6:20 and Agnes arrives at 6:40.