queneing problem. monte carlo simulation

Problem #3 (25 points) - Another Simulation Done By Hand On a given morning between 7:00 AM and 7:30 AM, a person and a bus arrives at a bus stop in accordance to the arrival-time distributions below. Arrival Time For The Person For The Bus 7:00 AM 0.05 0. 10 7:05 AM 0. 10 0. 15 7:10 AM 0. 15 0.20 7:15 AM 0.20 0.25 7:20 AM 0.25 0. 15 7:25 AM 0. 15 0. 10 7:30 AM 0. 10 0.05 a.) (12 points) Using the following twenty random numbers (ten for the person and ten for the bus) run a 10-day simulation and determine from this simulation the probability that the person catches the bus on a given morning, assuming that the person catches the bus whenever the person arrives before or at the same time as the bus arrives. Run Random Number For | Random Number For Number Person's Arrival Time Bus's Arrival Time 1 0.2245 0.1134 0.6533 0.7821 0.3312 0.9210 4 0.9278 0.8300 0.8815 0.5703 6 0.1377 0.0898 7 0.5535 0.8632 8 0.0398 0.4318 0.1845 0.9729 10 0.4422 0.2934 b.) (13 points) Compute the theoretical probability that the person catches the bus based on the arrival time pmf's given above for the person and bus