1. Bayesian Prediction [18 marks; 2 marks per part] Suppose you visit a province where license plates numbers are numbered sequentially. After seeing some cars go by on the road and reading their license plate numbers, you wonder: how many cars in total are there? What might the next number I see be? To formalize the problem, we assume that all cars in the province are numbered from 1 to L, where L is the largest licence plate number. Let M be the largest possible value of L. To make things simple, we'll assume that license plate numbers are three digits, so that M = 999. We assume that all values of L are equally likely, so our prior for L is a uniform distribution from 1 to M. Furthermore, we assume that, when we see a new car, we are equally likely to see any of the L cars out there, so the likelihood of seeing licence plate number X is also uniform. Our observations will be the numbers X, of the N cars we see go by. To specify the model, we dene ; A