Suppose a coffee shop opens at 7 am, and customers arrive at the shop following a Poisson process with a rate of 5 customers per hour. Let X denote the waiting time (in minutes) until the first customer arrives. (a) What is the pdf of X? Name the distribution if it has a name. (b) What is the probability that the owner of the coffee shop has to wait for more than 15 minutes before a first customer arrives? (c) What is the probability that the owner of the coffee shop has to wait for more than 20 minutes before a first customer arrives given that they haven't seen any customer for more than 15 minutes?