Please note that the deadline is strict! Suppose that new international students arrive in London according to a Poisson process of rate = 2 per day. Compute the expected time until the 100th student arrives. What is the probability that the time between the arrival of the 200th and the 201st student exceeds 2 days? Do you think we are working with a reasonable model here? How could you improve this model? Let N denote an inhomogeneous Poisson process with intensity function (t) = t + exp(t) for t 0. 1. Find P(N2 ?? N1 = 0). 2. Find P(N1:4 = 2;N2:3 = 3) and comment on your result. Let G = 0@ ??1 1 0 0 ??1 1 1 0 ??1 1A denote the generator of a continuous-time Markov chain. Find the stationary distribution . Question 3 [ 5 marks ] Question 2 [ 4 marks ] Question 1 [ 3 marks ] —Markov process in continuous-time: Poisson Process compound Poisson process with standard normally distributed jump sizes on the time interval [0; T]. (Please note that you do not need to implement these algorithms on a computer, you are only asked to state and describe them here. You may assume that you can simulate random variables from any distribution you need directly, but please state clearly all assumptions you make.) write down an algorithm to simulate a