Answer Happy

You observe the number of goals scored by a team you follow in n football matches {41, ..., yn}. The rate of scoring is related to the strength of the team as e Assuming each game is independent, the data can be assumed to follow a Poisson distribution i.e.: yi" Poisson (eº). iid (a) Derive the log-likelihood as a function of e. (b) Derive the score as a function of e. (c) Derive the observed Fisher Information as a function of O. (d) Show that the expected Fisher Information is [3] ] [3] [3] E[T(0)] = ne = [3] (e) Derive the Maximum Likelihood Estimator of e. [5] (f) Calculate an approximate 95% confidence interval for 0, if n = 10 and y = 150.4. [3] (g) Describe in detail how would you calculate a Bootstrapped 95% confidence interval for the strength of your team? [5] [Total 25 marks]