Problem 3 You have a bar that you have not been able to open in the last year as a result of the health contingency. However, as a result of the progress in vaccination and control of the pandemic, you are preparing the health protocols to be able to operate again. In particular, you have determined that the number of people arriving at your bar can be modeled as a Poisson Process with a rate of 20 people per hour. Once a person arrives at the bar, they stay until it closes. Thanks to the delay in the curfew of the Metropolitan Region announced as of September 1, the bar has its doors open from 6:00 p.m. to 12:00 a.m. a) What is the expected time of arrival of the first person at the bar? What is the variation in the time it takes for the first person to arrive? b) (2 points) What is the probability that 30 people will arrive between 19:00 and 21:00? What is the probability that at least 40% of the audience will arrive in the first third of the night on an average night? c) (2 points) If 43 people are known to have arrived at 9:00p.m., what is the probability that between 6:00 p.m. and 8:00 p.m. Have 30 people arrived? d) (2 points) What is the probability if 55 people are known to have arrived at 9:00 p.m. e) (3 points) What is the probability that person number 50 will arrive if it is done after 8:00 p.m., if it is known that between 7:00 p.m. and 9:00 p.m. 35 people arrived, and between 8:00 p.m. and 10:00 p.m. 45 arrived? Problem 3 You have a bar that you have not been able to open in the last year as a result of the health contingency. However, as a result of the progress in vaccination and control of the pandemic, you are preparing the health protocols to be able to operate again. In particular, you have determined that the number of people arriving at your bar can be modeled as a Poisson Process with a rate of 20 people per hour. Once a person arrives at the bar, they stay until it closes. Thanks to the delay in the curfew of the Metropolitan Region announced as of September 1, the bar has its doors open from 6:00 p.m. to 12:00 a.m. a) What is the expected time of arrival of the first person at the bar? What is the variation in the time it takes for the first person to arrive? b) (2 points) What is the probability that 30 people will arrive between 19:00 and 21:00? What is the probability that at least 40% of the audience will arrive in the first third of the night on an average night? c) (2 points) If 43 people are known to have arrived at 9:00p.m., what is the probability that between 6:00 p.m. and 8:00 p.m. Have 30 people arrived? d) (2 points) What is the probability if 55 people are known to have arrived at 9:00 p.m. e) (3 points) What is the probability that person number 50 will arrive if it is done after 8:00 p.m., if it is known that between 7:00 p.m. and 9:00 p.m. 35 people arrived, and between 8:00 p.m. and 10:00 p.m. 45 arrived
