Probability Exam—January 2019 Syllabus

Transcript

1 —January 2019 Probability Exam three-hour exam consists of 30 multiple-choice questions and is The Probability Exam that is a administered as a computer -based test. The purpose of the syllabus for this examination is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial of the supporting calculus is assumed. Additionally, a very science is emphasized. A thorough command basic knowledge of insurance and risk management is assumed. A table of values for the normal distribution is available below for candidates to download and will be included with the examina tion. Since the table will be included with the examination, candidates will not be allowed to bring copies of the table into the examination room. section on this exam’s home page for any changes to the exam or syllabus. Updates Check the The ranges of weights shown are intended to apply to the large majority of exams administered. On occasion, the weights of topics on an individual exam may fall outside the published range. Candidates should also recognize that some questions may cover multiple learning outcomes. Each multiple -choice problem includes five answer choices identified by the letters A, B, C, D, and E, only one of which is correct . Candidates must indicate responses to each question on the computer. As part of the computer -based testing process, a few pilot questions will be randomly placed in the exam (paper and pencil and computer -based forms). These pilot questions are included to judge their future exams, but they will not effectiveness for be used in the scoring of this exam. All other questions will be considered in the scoring. All unanswered questions are scored incorrect. Therefore, candidates should answer every question on the exam. There is no set requirement for the distribution of correct answer s for the multiple- choice preliminary examinations. It is possible that a particular answer choice could appear many times on an examination or not at all. Candidates are advised to answer each question to the best of their ability, independently from how they have answered other questions on the examination. Since the CBT exam will be offered over a period of a few days, each candidate will receive a test form composed of questions selected from a pool of questions. Statistical scaling methods are used to ensure within reasonable and practical limits that, during the same testing period of a few days, all forms of the test are comparable in content and passing criteria. The methodology that has been adopted is used by many credentialing programs that give multiple forms of an exam. Recognized by the Canadian Institute of Actuaries

2 LEARNING OUTCOMES 1. T opic: General Probability (10 -17%) Learning Objectives The Candidate will understand basic probability concepts. Learning Outcomes The Candidate will be able to: a) Define set functions, sample space, and events. Define probability as a set function on a collection of events and state the basic axioms of probability. b) Calculate probabilities of mutually exclusive events. c) Calculate probabilities using the addition and multiplication rules. d) Define independence and calculate probability of independent events. e) Calculate probabilities using combinatorics, such as combinations and permutations. f) Define and calculate conditional probabilities. g) State Bayes Theorem and use it to calculate conditional probabilities. 2

3 2. iables (40 -47%) Topic: Univariate Random Var Learning Objectives The Candidate will understand key concepts concerning discrete and continuous univariate random variables (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, normal, and mixed) and their applications. Learning Outcomes The Candida te will be able to: Explain and apply the concepts of random variables, probability and probability density a) functions, cumulative distribution functions. Calculate conditional probabilities. b) c) Explain and calculate expected value, mode, median, percentile, and higher moments. d) Explain and calculate variance, standard deviation, and coefficient of variation. e) Define probability generating functions and moment generating functions and use them to calculate probabilities and moments. f) Determine the sum of independent random variables (Poisson and normal). g) Apply transformations. 3

4 3. Topic: Mult ivariate Random Variables (40 -47%) Learning Objectives The Candidate will understand key concepts concerning multivariate random variables (including the bivariate normal) and their applications. Learning Outcomes The Candidate will be able to: a) Explain and perform calculations concerning joint probability and probability density functions and cumulative distribution functions. b) Determine conditional and marginal probability and probability density functions, cumulative distribution functions. Calculate moments for joint, conditional, and marginal random variables. c) d) Explain and apply joint moment generating functions. e) Calculate variance and standard deviation for co nditional and marginal probability distributions. f) Calculate joint moments, such as the covariance and the correlation coefficient . g) Determine the distribution of a transformation of jointly distributed random variables. Determine the distribution of order statistics from a set of independent random variables. h) Calculate probabilities and moments for linear combinations of independent random variables. i) State and apply the Central Limit Theorem . 4

5 REFERENCES Suggested Texts There is no single required text for this exam. The texts listed below may be considered as representative of the many texts available to cover material on which the candidate may be examined. Texts are added -to-date. Th e addition or deletion of a textbook and deleted as part of a regular process to keep the list up does not change the bank of questions available for examinations. There is no advantage to selecting a text recently added or not using a text recently removed. Not all the topics may be covered adequately by just one text. Candidates may wish to use more than one of the following or other texts of their choosing in their preparation. Earlier or later editions may also be adequate for review. • A F irst Course in Probability (Ninth Edition), 2012 , by Ross, S.M., Pearson/Prentice Hall, ISBN: 978 - 0321794772 Chapters 1–8 , • Mathematical Statistics with Applications (Seventh Edition), 2008, by Wackerl y, D., Mendenhall III, W., Scheaffer, R., Thomson Brooks/Cole ISBN: 9 78-0495110811 , Chapters 1 -7. • Probability for Risk Management, (Second Edition), 2006, by Hassett, M. and Ste wart, D., ACTEX, 11. ISBN: 978 -156698-2, Chapters 1– • nd Statistical Inference (Ninth Edition), 2014, by Hogg, R.V., Tanis, E.A., and D. Probability a Zimmerman, Prentice Hall, ISBN: 978 -0321923271, Chapters 1 –5. with Applications: A Problem S • olving Text, (Second Edition) 2015 , by Probability and Statistics Asimow, L. and Maxwell, M., ACTEX , ISBN: 978-1-62542-472-3 , Chapters 1– 8 (excluding section 8.5) Other Resources The candidate is expected to be familiar with the concepts introduced in “ Risk and Insurance ”. Tables for Exam P Exam P Sample Questions Solutions and Online Sample Exam P The Society of Actuaries (SOA) is interested in supporting candidates as they prepare for the preliminary exams. Available at no To that end the SOA has launched an online sample exam for Exam P (Probability). cost the sample exam selects questions and solutions in an online exam experience that resembles the computer -based testing employed for most of the SOA’s pr eliminary exams. Questions have been coded to meet the Exam P learning objectives and ensure candidates receive a balanced yet randomized set of questions each time they repeat the sample exam. The current set of questions is drawn from the existing of sample questions. set 5

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