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2. You observe the number of goals scored by a team you follow in n football matches {41, ... , Yn}. The rate of scoring
Posted: Mon May 09, 2022 12:04 pm
by answerhappygod
- 2 You Observe The Number Of Goals Scored By A Team You Follow In N Football Matches 41 Yn The Rate Of Scoring 1 (97.45 KiB) Viewed 34 times
2. 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 eº. Assuming each game is independent, the data can be assumed to follow a Poisson distribution i.e.: y; " Poisson (eº). iid [3] [3] (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] E[T(O)] = ne = [3] (e) Derive the Maximum Likelihood Estimator of 0. [5] (f) Calculate an approximate 95% confidence interval for O, if n = 10 and y = 150.4. [3] (9) Describe in detail how would you calculate a Bootstrapped 95% confidence interval for the strength of your team? [5] (Total 25 marks]