4. THE LIGHTHOUSE PROBLEM 4. This problem was set by Steve Gull to first year Cambridge students It contrasts the Bayesian approach with an estimator-based approach. A lighthouse is situated at unknown coordinates (To, yo) with respect to line y = 0. It sends a series of /V flashes in random directions, and these the coastline at positions x,; i = 1. .. N. Only the positions of the arrive not the directions, nor the intensities, are recorded. Using a Bayesian at posterior distribution of co, yo- Now focus only on the unknown To. Define a suitable estimator, i, observed ri. Work out the probability distribution for 2. You may need t of the Central Limit Theorem, for the pdf of repeated trials of the same may also find this useful: de = elkro-klyn Comment. You can get some extra points if you simulate this process, compute the and also show the estimator