The students in the electrical and computer engineering department of a certain college arrive at the departmental lounge to view the video of the lecture for a particular course according to a Poisson process with a rate of 5 students per hour. The person in charge of the operating the VCR will not turn the machine on until there are at least 5 students in the lounge.
a. Given that there is currently no student in the lounge, what is the expected waiting time until the VCR is turned on?
b. Given that there is currently no student in the lounge, what is the probability that the VCR is not turned on within one hour from now?