Q1. Suppose that new international students arrive in London according to a Poisson process of rate λ = 2 per day.
a) Compute the expected time until the 100th student arrives.
b) What is the probability that the time between the arrival of the 200th and the 201st student exceeds 2 days?
c) Do you think we are working with a reasonable model here? How could you improve this model?
Q2. Let N denote an inhomogeneous Poisson process with intensity function λ(t) = t + exp(t) for t ≥ 0.
a. Find P(N2 - N1 = 0).
b. Find P(N1.4 = 2, N2.3 = 3) and comment on your result