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Examiners’ commentaries 2017 Examiners’ commentaries 2017 ST104b Statistics 2 Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2016–17. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide and the Essential reading references Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2014). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refer to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section. General remarks Learning outcomes At the end of this half course, and having completed the Essential reading and activities, you should be able to: • apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments • explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform tests in a number of different settings • demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems. Format of the examination The examination is two hours long and you must answer all four questions. Question 1, for 40% of the marks, is a compulsory question with several parts. It is designed to test general knowledge and understanding of the whole syllabus. Here candidates are expected to give reasoned answers, with some explanation, avoiding one-word responses which will never be given any marks. More emphasis is given to understanding than to knowledge. Candidates should answer the first part of this question (true or false statements) either by proving that the statement is true or false or, in the case of a false statement, providing a counterexample. It is not sufficient to just provide the correct answer (no credit is given for this); an explanation is required. Furthermore, 1
ST104b Statistics 2 when trying to show that a certain statement is true, it is not sufficient to show that the statement is true in a very specific case. The other three questions are also compulsory and account for 20% of the total marks each. They are meant to test a greater depth of knowledge on parts of the syllabus. They are also longer and examine the ability to apply general knowledge and concepts to specific problems. How to prepare for the examination It is hard to emphasise enough that memorising answers to past examination questions is not the best way to study for this paper. It is important for candidates to understand the material they write down, and to be able to develop it all from scratch as they write it. Often, there are several ways to obtain good marks for a question. If you cannot solve a certain section of a question you might still get full marks for subsequent sections as long as your reasoning is correct. A very good mathematics background is extremely important. The course can be divided into a probability and distribution theory part and a statistics part. A mathematics background is important for both but especially for the probability and distribution theory part. You should ensure you have an understanding of all parts of the half course. Specialising is a bad strategy as all questions are compulsory and there is no choice. In the 2017 examination paper, Question 4 (c) (for both zones) involved method of moments estimation. In general, candidates did poorly overall in this question, possibly because candidates had put more emphasis on studying maximum likelihood estimation instead. See Section 7.7 of the subject guide for more details on method of moments estimation. Also, in Question 4 (c) many candidates failed to find the correct maximum likelihood estimator as they differentiated the (log-)likelihood function rather than using Question 4 (b) directly. More details are provided in the comments for both zones. Candidates also did surprisingly poorly on the true and false questions (both zones). There were two main reasons for this. On the one hand, candidates often did not use the correct definitions (for example, a common mistake is to confound the notions of independence and disjointness). On the other hand, many candidates used a specific example to ‘prove’ a true statement. When a statement is true, no further assumptions should be made on top of the ones given in the question. This is in contrast with false statements, where a single counterexample suffices. The paper is light on computations, as questions are answered with the use of a basic calculator only. Key steps to improvement You should understand all parts of the half course without exception. Remember that all questions in the paper are compulsory. Another reason why you should understand all parts of the course is that you should not expect to get very similar questions compared to previous years’ papers. You should be able to write down or discuss definitions or models used in the syllabus. It is important that you have the necessary mathematical skills. This means that you should understand your mathematics courses well too. Routine computations are less important and you should spend more time understanding the concepts. Understanding concepts means being able to apply them, sometimes even in combined situations. As stated earlier, the ST104b Statistics 2 examinations are not heavy in calculations. Probability is the most important part of the half course as everything else depends on it. You must have a thorough understanding of all concepts. You should avoid making elementary mistakes which demonstrate a lack of understanding and are hence heavily penalised by the examiners. These 2

ST104b Statistics 2 Examiners’ commentaries 2017 ST104b Statistics 2 Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2016–17. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide and the Essential reading references Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2014). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refer to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section. Comments on specific questions – Zone A Candidates should answer all FOUR questions: QUESTION 1 of Section A (40 marks) and all THREE questions from Section B (60 marks in total). Candidates are strongly advised to divide their time accordingly. Section A Answer all five parts of question 1 (40 marks). Question 1 (a) For each one of the statements below say whether the statement is true or false, and explain your answer. Throughout this question A and B are events such that 0 < P (A) < 1 and 0 < P (B) < 1. i. If A and B are independent events then P (A ∩ B) = 0. ii. If A ⊂ B, then P (A) ≤ P (B). iii. The event A is independent of ∅. iv. It holds that: P (A ∪ B) ≥ P (A) + P (B) 2 . v. If k > 1 and X is a random variable, then Var(kX) = k Var(X). (10 marks) 4