\f3. Suppose the arrival of bus 222 at the bus stop at Mawson Lakes is a homogeneous Poisson process {N](t}} with arrival rate A], and the arrival of bus 411 at the same bus stop is a homogeneous Poisson process {N2(t)} with arrival rate M. In the simulation part of this question. time is measure in hours and you are looking at bus arrivals over (0. 2], that is. over 2 hours. You ma)r use R or Matlab to do the simulation. (a) What. is the distribution of the number of arrivals of any has over the interval (0, t]? Please cite the relevant results to justify your answer. (b) Suppose T is the time to the arrival of the rst 222 bus and S is the time to the arrival of the rst 411 bus. 'What is the probability that the rst 222 bus arrives before the rst 411 bus? (Note: This is simple the probabilityF calculation that PIT 4: S], but some conditioning is required.)