A policewoman on the evening shift writes a Poisson mean 6 number of tickets per hour. 2/3’s of these are for speeding and cost $100. 1/3’s of these are for DWI and cost $400. (a) Find the mean and...

A policewoman on the evening shift writes a Poisson mean 6 number of tickets per hour. 2/3’s of these are for speeding and cost $100. 1/3’s of these are for DWI and cost $400. (a) Find the mean and standard deviation for the total revenue from the tickets she writes in an hour. (b) What is the probability that between 2 a.m. and 3 a.m. she writes five tickets for speeding and one for DWI. (c) Let A be the event that she writes no tickets between 1 a.m. and 1:30, and N be the number of tickets she writes between 1 a.m. and 2 a.m. Which is larger P(A) or P(A|N = 5)? Don’t just answer yes or no, compute both probabilities.