You and your partner are the owners of a company that specializes in remodeling houses and interior decoration. You would like to track the amount of complaints you get a month, but do not know how. Your cousin currently goes to college and tells you “I can help out.” Using the data of the past 20 years, she determines that the mean number of complaints a month is 1.5 and that it is reasonable to assume that it follows a Poisson distribution.
a) What is the variance of the number of complaints in any given month?
b) What is the probability that you will get exactly three complaints next month?