Students at Medipol access MEBIS system at a rate of 10 students/minute and the number of students accessing the system follows a Poisson distribution. We start our clock and observe students accessing the MEBIS system. Determine the followings: (a) (5 Pts.) What is the probability that the first student accessing the MEBIS system is between 3 and 4 minutes? (b) (5 Pts.) What is the probability that the 1000th student accessing the MEBIS system is between 1 and 1.5 hours? (c) (5 Pts.) We set our clock at 8:00 AM and start observing the student accessing MEBIS. However, we want to see less student accessing the system once time passes by. Pro- pose a distribution and plot its PDF. You can make necessary assumptions about the parameters you need. (d) (10 Pts.) Let X represent the time that the first student access the MEBIS system. If Y = XCX, determine the PDF of Y. (e) (10 Pts.) Determine P(Y> 10min) via two different approaches.