2. You observe the number of goals scored by a team you follow in n football matches {91...., Yn}. The rate of scoring i

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2 You Observe The Number Of Goals Scored By A Team You Follow In N Football Matches 91 Yn The Rate Of Scoring I 1 (54.61 KiB) Viewed 30 times

2. You observe the number of goals scored by a team you follow in n football matches {91...., 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.: y d Poisson (eº). (a) Derive the log-likelihood as a function of O. (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] ELI(0)] = ne [3] (e) Derive the Maximum Likelihood Estimator of 0. [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]