- Please Answer All The Ff Questions 1 (72.23 KiB) Viewed 27 times
PLEASE ANSWER ALL THE FF QUESTIONS:
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answerhappygod
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PLEASE ANSWER ALL THE FF QUESTIONS:
PLEASE ANSWER ALL THE FF QUESTIONS:
2. You observe the number of strikes {x1, ..., xn} scored by a bowler in n games. In each game, the bowler has a = 10 attempts at a strike and the probability of a strike is related to the skill a > 0 of the bowler as . Assuming each attempt and each game are independent, the data can be assumed to follow a Binomial distribution i.e.: xi id Binomial (a, ). (a) Derive the log-likelihood as a function of 1. (b) Derive the score as a function of 1. (c) Derive the observed Fisher Information as a function of 1. (d) Show that the expected Fisher Information is [3] [3] [3] na ET ()] = 1(1 + 1)2 [3] (e) Derive the Maximum Likelihood Estimator of l. [5] (f) Estimate the standard error of  using a Normal approximation to the like- lihood, if n = 20, a = 10,8 = 9.15. [3] (g) Describe in detail how would you calculate a Jackknife estimate of the standard error of your estimate of the skill î for the bowler? You do not need to perform the calculations. [5]
2. You observe the number of strikes {x1, ..., xn} scored by a bowler in n games. In each game, the bowler has a = 10 attempts at a strike and the probability of a strike is related to the skill a > 0 of the bowler as . Assuming each attempt and each game are independent, the data can be assumed to follow a Binomial distribution i.e.: xi id Binomial (a, ). (a) Derive the log-likelihood as a function of 1. (b) Derive the score as a function of 1. (c) Derive the observed Fisher Information as a function of 1. (d) Show that the expected Fisher Information is [3] [3] [3] na ET ()] = 1(1 + 1)2 [3] (e) Derive the Maximum Likelihood Estimator of l. [5] (f) Estimate the standard error of  using a Normal approximation to the like- lihood, if n = 20, a = 10,8 = 9.15. [3] (g) Describe in detail how would you calculate a Jackknife estimate of the standard error of your estimate of the skill î for the bowler? You do not need to perform the calculations. [5]
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