We have a simple data set for the number of years that transfer students took to complete their degree. 45 students completed their degree in 1 year, 38 students completed their degree in two years and 27 students took longer than two years.

(a) Suppose that the number of years follows a geometric distribution. Calculate the MLE of the parameter p.

(b) Suppose that we wanted to use a more general model that had parameters (p1, p2, p3): the probability of finishing in one, two, and more than two years respectively. Find the MLE of the three parameters from this data.

(c) Now, looking over the records, we find that there are 20 more students who took more than one year (we dont know when they graduated).i. Calculate a new MLE using the geometric model in part (a).ii. Calculate a new MLE using the general model from part (b).