1. We have been hired by the UCCS to study the frequency with which students are referred to the Student Health Center as an emergency intervention case. The model we will use is that the number of students referred in a month is a Poisson Random Variable with some mean number of students lambda that are referred each month. Why does Poisson seem appropriate here? 

a. Before we make our observations we are going to develop a Bayes approach to this problem, which means we need to make some prior assumptions about the possible values of lambda that could be in play and how likely they are. Do this. Note that while the Poisson variable gives integers; the mean value is a positive real number. 

b. Now suppose that in the first month of our consulting 2 students are referred to the Student Health Center. Use this observation to update our prior estimate to a posterior estimate. 

c. In the second month, 0 students were referred. Update to a new posterior estimate.

d. Using this new posterior estimate, construct a 60% credible interval for the values lambda could have.