6.2 Poisson distribution (Value: 29 points) Instructions: In this task, youwill work with another of the discrete probability distributions. You will calculate the Poisson distribution. You should present the necessary processes to support the response of the exercises and round the final results-not the intermediate values that appear during the calculations-to two decimal places, when necessary. Exercise #1 1) Explains when the Poisson probability distribution is used. (3 points) Exercise #2 1) Consider a Poisson random variable with ?? = 2.5. Use Poisson's formula to calculate the following probabilities: a) P(0) (3 points) b) P(2) (3 points) c) P(1) (3 points) Exercise #3 1) Using the Poisson distribution table, determine the probability when: a) ??=0.8, if x= 2 (2 points) b) ??=5.0, if x= 5 (2 points) c) ??= 2.5, if x= 3 (2 points) Exercise #4 2) The number x of people admitted to an intensive care unit in a particular hospital, on any given day, has a Poisson probability distribution with an average equal to five (5) people per day. What is the probability that the number of people admitted to an intensive care unit, on a particular day, is three (3)? Solve using Poisson's formula (Mendenhall et al. , 2015). (5 points) Exercise #5 1) Calculate with a) the formula and b) the table, the Poisson probability when = ??4, if x = 8. Certify that with both methods you get the same result. (6 points)