A university offers a new degree on Data Science and wants to predict the proportion of students that will graduate with a first class honour degree. Based on data from similar degrees staff believe that on average one third of students will graduate with first class and the mode is 1 in 4. (a) Let be the probability that a student of the new Data Science degree graduates with a first class honour degree. Specify a beta distribution that reflects the staff's prior belief about . (b) From the first 50 graduates, 15 obtained a first class honour degree. What is the posterior distribution for ? Compute the mean and the mode. (c) The university has a target that 50% of the students in the new BSc degree achieve a first honour degree. What is the probability of meeting the target?