Question 2 (10 pts) A police officer observes pedestrians arriving at a crosswalk. Pedestrians arrive at a rate of 2 per minute, according to a Poisson Process. If no pedestrian arrives within 2 minutes of the last pedestrian who arrived, the police officer leaves (In the case of the first pedestrian, the police officer will leave if the first pedestrian doesn't arrive within 2 minutes of the start time). a) Find the probability that the police officer doesn't leave before the first 4 pedestrians arrive at the crosswalk. (Hint: Use the memoryless property of exponential distributions) (5 pts). b) A second police officer joins to observe the crosswalk starting when the first pedestrian arrives at the crosswalk. Once the police officer starts observing, he or she will leave if it takes more that 9 minutes for the tenth pedestrian to arrive. Find the probability that the second police officer leaves. (5 pts)