The speed limit on Gunghalin Drive in Canberra between Barton Highway and the Glenloch interchange is 90km/h. Ben frequently drives on Gunghalin Drive and typically drives at a constant speed of 90km/h (that is, at the speed limit) on this section of road. One day, he passes 3 cars and gets passed by 17 cars on this section of road. Suppose that car speeds on this section of road are normally distributed with unknown mean / and known standard deviation o = 4.5. Let s = 3 denote the number of cars that Ben overtakes and let their unobserved car speeds be y1, y2, y3. Let t = 17 denote the number of cars that overtake Ben and let their unobserved car speeds be y4, y5, .....920. (a) 3 marks Assign the unknown mean p a flat prior density. Write down the mathematical expression for the posterior density of / (that is, p(ulo, s, t, y)) up to a proportionality constant. Hint: the actual car speeds yi (i = 1, ..., 20) are not observed, but if Ben passes say Car A, then we know that the speed of Car A must be less than 90km/hr. Similarly if Car B passes Ben, then we know that the speed of Car B must be greater than 90km/hr