Mary is counting the number of delivery trucks passing in front of her house every day between 8 am and 4 pm. Based on her observations, Mary believes that trucks arrive according to a Poisson process with the average number of 4 trucks per day (between 8 am and 4 pm). (Numerical answers to questions below should be reported to 4 decimal places). a)(4 points) Mary counts the number of trucks every day over a period of 7 days. Find the probability that Mary will see exactly 2 trucks on one of the days and exactly 3 trucks on four of the days and exactly 5 trucks on two of the days. b) (3 points) In a period of 7 days, what is the expected number of days Mary will see either 2 or 3 trucks? c)(4 points) Mary remembers that in a period of 7 days there where only 3 days with 5 trucks. What is the probability that each of the other 4 days had 2 trucks? d)(4 points) Mary remembers that on Monday there was at least one delivery truck. What is the probability that the rst truck arrived before 12:00 pm