Every year in the run-up to Christmas, many people in the UK speculate about whether there will be a 'White Christmas', that is, snow on Christmas Day. There are many definitions of what exactly constitutes an official 'White Christmas'. For the purposes of this question, assume that 'White Christmas' simply means snow or sleet falling in Glasgow sometime on Christmas Day. (a) Suppose that represents P(next Christmas is a White Christmas). What is your assessment of the most likely value for 0? Also, what are your assessments for the upper and lower quartiles of 0? Briefly describe the reasoning that you used to make your assessments. (b) Suppose that another student, Chris, assesses the most likely value of to be 0.25, the lower quartile to be 0.20 and the upper quartile to be 0.40. It is decided to represent Chris's prior beliefs by a Beta(a, b) distribution. Use Learn Bayes to answer the following. (i) Give the parameters of the Beta(a, b) distribution that best matches Chris's assessments. (ii) Is the best matching Beta(a, b) distribution that you specified in part (b)(i) a good representation of Chris's prior beliefs? Why or why not? (c) In the years 1918 to 2009, a period of 92 years, there were 11 Christmas Days in Glasgow that were officially 'white'. (Assume that the probability of a White Christmas is independent of the weather conditions for any other Christmas Day. Also assume that there has been no change in climate and hence that the probability of a White Christmas has not changed during this period.) (ii) Give a 99% highest posterior density credible interval for 0. Why is this interval not the same as the 99% equal-tailed credible interval? (iii) The posterior for 0 is a beta distribution. Why? Calculate the parameters of the beta distribution (