Tiêu đề ST104B - Statistics 2 - 2019 Examiners Commentaries.pdf ✅

ST104b Statistics 2 is true in a very specific case – this does not prove the statement is true, you must show the statement holds in all circumstances. 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 overemphasise 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. 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 include the following. • Calculating probabilities outside the range 0 to 1. Should that happen because of a calculation mistake, candidates must state that they think a mistake was made. • Calculating negative variances or sums of squares. Should that happen because of a calculation mistake, candidates must state that they think a mistake was made. • Finding a correlation outside the range −1 to 1. • Confusing independent and mutually exclusive events. You should spend a sufficient amount of time studying the distinction between these. You should get familiar with the logical thinking needed to answer the first part of Question 1. 2
Examiners’ commentaries 2019 When there is no evidence to reject a null hypothesis it does not mean that there is evidence to accept it. You should have a clear understanding of conditional probabilities. Examination revision strategy Many candidates are disappointed to find that their examination performance is poorer than they expected. This may be due to a number of reasons, but one particular failing is ‘question spotting’, that is, confining your examination preparation to a few questions and/or topics which have come up in past papers for the course. This can have serious consequences. We recognise that candidates might not cover all topics in the syllabus in the same depth, but you need to be aware that examiners are free to set questions on any aspect of the syllabus. This means that you need to study enough of the syllabus to enable you to answer the required number of examination questions. The syllabus can be found in the Course information sheet available on the VLE. You should read the syllabus carefully and ensure that you cover sufficient material in preparation for the examination. Examiners will vary the topics and questions from year to year and may well set questions that have not appeared in past papers. Examination papers may legitimately include questions on any topic in the syllabus. So, although past papers can be helpful during your revision, you cannot assume that topics or specific questions that have come up in past examinations will occur again. If you rely on a question-spotting strategy, it is likely you will find yourself in difficulties when you sit the examination. We strongly advise you not to adopt this strategy. 3
ST104b Statistics 2 Examiners’ commentaries 2019 ST104b Statistics 2 Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2018–19. 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 parts of question 1 (40 marks). Question 1 (a) For each one of the statements below say whether the statement is true or false, justifying your answer. i. For any three events A, B and C, if P (A ∩ B ∩ C) = P (A) P (B) P (C) then A, B and C are independent. ii. For any two random variables X and Y it holds that: Var(X − Y ) = Var(X) + Var(Y ). iii. The event A is independent of Ac . iv. The product of two unbiased estimators of the same parameter is also an unbiased estimator of the same parameter. v. Two fair dice are thrown and let A = {the sum of the dice is 2, 4 or 5} and B = {the dice show a total score that is even}. The events A and B are independent. (10 marks) 4