Starting at 9 a.m., students arrive to class according to a Poisson process with parameter λ = 2 (units are minutes). Class begins at 9:15 a.m. There are 30 students.
(a) What is the expectation and variance of the number of students in class by 9:15 a.m.?
(b) Find the probability there will be at least 10 students in class by 9:05 a.m.
(c) Find the probability that the last student who arrives is late.
(d) Suppose exactly six students are late. Find the probability that exactly 15 students arrived by 9:10 a.m.
(e) What is the expected time of arrival of the seventh student who gets to class?