STOCHASTIC PROCESS

QUESTION 5 Suppose that meter taxis commute from city A to city B at a Poisson rate A = 3 per day. (5.1) If the number of passengers, including the driver, in each taxi is independent and takes on the values 11 2, 31 415 with probabilities ill, (13, D.3,.2, ELI, then what is the expected value and the variance of the number of individuals who have commuted from city A to city B during a xed onerweek (T days} period? Show all calculation steps. (16} (5.2) Find the approximate probability that at least 3GB individuals have commuted from city A to city 3 during two weeks time. (8}