Australian School Of Business Actuarial Studies

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Australian School of BusinessActuarial StudiesACTL2002PROBABILITY AND STATISTICS FOR ACTUARIESCOURSE OUTLINESESSION 1, 2011 2011The University of New South WalesSydney 2052 AustraliaThe original material prepared for this guide is copyright. Apart from fair dealing forthe purposes of private study, research, criticism or review, as permitted under theCopyright Act, no part may be reproduced by any process without writtenpermission. Enquiries should be addressed to the Head of School, ActuarialStudies, UNSW, Sydney 2052ACTL2002 – Probability & Statistics for ActuariesPage- 1

Dear Students,Welcome to ACTL2002 / 5101 Probability and Statistics for Actuaries.For undergraduate students, this course is one of eight courses for the BComActuarial major. Most of you will be completing ACTL2001 FinancialMathematics (for Actuaries) in Session 1. In Session 2 you should all becompleting ACTL2003 Stochastic Models for Actuarial Applications.For postgraduate students, this course is one of eight courses covering theCore Technical subjects of the Institute of Actuaries offered in the Master ofActuarial Studies. Some of you may already have completed some of thecourses ACTL5101 Financial Mathematics for Actuaries, ACTL5104 ActuarialStatistics and ACTL5105 Life Insurance and Superannuation Models. If this isthe first actuarial course you are taking, you will find that you will have to adjustto the study load.Probability is the branch of science concerned with the mathematical modelsand techniques for making quantitative inferences about uncertainty. Statisticsdeals with the collection and the analysis of data. Together, these twodisciplines provide us with fundamental tools to analyse risk and manage thefinancial consequences of future uncertainties. This course provides you with afoundation in the probability models and statistical techniques required foranalysing risks in modern financial markets. It provides a foundation for coursesin your actuarial major in the final years of undergraduate study at UNSW. Ihope you find the course challenging and interesting.This course outline has details of the course requirements, course aims andlearning outcomes, content, teaching methods, assessment tasks, texts andreadings, and expectations. Please read it carefully and thoroughly, as it will beassumed that you are familiar with the contents.If you have any questions about the course at any time then please contact me.Ralph StevensACTL2002 – Probability & Statistics for ActuariesPage- 2

TABLE OF CONTENTS1STAFF CONTACT DETAILS42COURSE DETAILS42.12.22.32.42.52.6Teaching Times and LocationsUnits of CreditSummary of CourseCourse Aims & Relationship to other CoursesStudent Learning OutcomesCoverage of IAAUST Learning Outcomes555573 LEARNING AND TEACHING ACTIVITIES83.13.288Approach to Learning and Teaching in the CourseLearning Activities and Teaching Strategies4 ASSESSMENT94.14.24.391012Formal RequirementsAssessment DetailsLate Submission5 ACADEMIC HONESTY AND PLAGIARISMSchool of Actuarial Studies Policy on Plagiarism13136 COURSE RESOURCES13TextbooksFormulae & TablesSoftwareCourse Blackboard Site131414147 COURSE EVALUATION AND DEVELOPMENT148 STUDENT RESPONSIBILITIES AND endanceSpecial Consideration and Supplementary ExaminationsGeneral Conduct and BehaviourOccupational Health and SafetyKeeping Informed9 ADDITIONAL STUDENT RESOURCES AND SUPPORT1710 KEY DATES AND STUDENT RESPONSIBILITIES SEMESTER 1, 20111811 COURSE SCHEDULEACTL2002 – Probability & Statistics for Actuaries19Page- 3

1STAFF CONTACT DETAILSThe Lecturers of this course are:StaffE-mailRoomTelephoneDr. Ralph StevensRalph.stevens@unsw.edu.auQuad 20729385 3566He is responsible for course administration, final assessment of the course and for thelectures and related teaching and learning. His consultation times are on Monday,10am to 11am until 2 June 2011. Additional exam preparation consultation times in theweek of 6 June 2011 will be advertised later.The tutors for this course areStaffE-mailConsultationVincent Tuvincenttu222@hotmail.comTuesday 1pm-2pmTimothy Yiptimothy.yip@unsw.edu.auTo be announcedThey are responsible for running the tutorials as well as marking the quizzes and theassignment. They will hold consultation in Quad 2082A (02 9385 8005). All tutors areavailable to all students, so please do not hesitate to visit them at your most convenienttime.Who should I contact? Questions about the lectures: Ralph Stevens during his consultation timeor by e-mail; Questions about tutorial problems: the tutors, Ralph Stevens, during hisconsultation times or by e-mail; Administrative enquiries about the course: Ralph Stevens, during hisconsultation time or by e-mail; Enquiries about undergraduate or postgraduate coursework programs inActuarial Studies: the director of Actuarial Programs (Dr. Bernard Wongbernard.wong@unsw.edu.au); Enrolment: ASB Student Centre.2 COURSE DETAILS2.1 Teaching Times and LocationsThis course will consist of three hours of lectures and a one hour tutorial per week.Lecture times and locations are as follows:Monday2:00 p.m. – 5:00 p.m.Biomedical Theatre DTimetables and locations are correct at time of printing. A full timetable of lectures andtopics is provided later in this course study guide. Any alterations to the lecture times orlocations will be advised in lectures and via Blackboard.Students should consult Blackboard on a regular basis, since assignment questionsand other course materials will be placed there. The web address is:http://lms-blackboard.telt.unsw.edu.auACTL2002 – Probability & Statistics for ActuariesPage- 4

TutorialsDuring the twelve weeks of tutorial classes each student will have to make one classpresentation, involving presenting the solution to a statistical problem, in his or hertutorial. You will find your allocated time and question on Blackboard. See Blackboardfor full details.Tutorials commence in Week 2.T09ATuesday9am-10amQuad 2052Mr Timothy YipT10ATuesday10am-11amQuad 2052Mr Timothy YipT14ATuesday2pm-3pmRedC 1040Mr Vincent TuT15ATuesday3pm-4pmRedC 1040Mr Vincent TuT15BTuesday3pm-4pmRedC 1041Mr Timothy YipM17A 1Monday5pm-6pmRedC M032Dr Ralph StevensStudents must attend the tutorial for which they are enrolled. Attendance will berecorded and count towards meeting the requirements to pass the course. If you wishto change your tutorial then you must lodge an application to change your tutorial timewith the Actuarial Studies office.In tutorials, we will implement interactive learning where participation is highlyencouraged. To get the most out of the tutorials, students should read lecture notesand textbooks and references and complete assigned homework problems in advanceof the tutorial.Peer-Assisted-Support-Scheme (PASS):In addition, an actuarial PASS program will be available to enhance student learning inthis course. It is highly recommended that you attend these sessions. Full details willbe posted on Blackboard.2.2 Units of Credit62.3 Summary of CourseThis course covers probability and statistics topics relevant to actuarial studies. Topicscovered include univariate/multivariate random variables, moments, probabilitygenerating functions, moment generating functions, marginal and conditionaldistributions, sampling distributions, estimation methods, hypothesis tests, regression,and analysis of variance. Examples relevant to actuarial studies, finance and insuranceare used to illustrate the application of the topics covered.2.4 Course Aims and Relationship to Other CoursesAt the end of the course students should be able to:A. Demonstrate an understanding of probability theory;B. Demonstrate an understanding of statistical theory;1For postgraduate students only.ACTL2002 – Probability & Statistics for ActuariesPage- 5

C. Use the software package R to undertake the basic statistical analysis taught inthe course;D. Express his/her views on, and understanding of, an aspect of probability andstatistics.This course covers probability and statistics at an introductory yet mathematicallyrigorous level with a strong foundation in mathematics. The assumed knowledge of thecourse is a good understanding of mathematics as covered in MATH1151 andMATH1152. Students with equivalent mathematics coverage at a very high grade inMATH1131 or MATH1141 or ECON1202 may also have the required mathematicalbackground. Consult the Course Coordinator if you do not have the requiredmathematical background.ACTL2002/5101 Probability and Statistics for Actuaries builds on the basic concepts ofprobability and statistics covered in ACTL1001 Actuarial Studies and Commerce. Thecourse will have applications in other courses in the actuarial major. More advancedmodels are covered in ACTL2003 Stochastic Models for Actuarial Applications. Thecourse is necessary knowledge for the more advanced coverage in ACTL3001Actuarial Statistics and ACTL3003 Insurance Risk Models.The course corresponds to the actuarial professional subject CT3 Probability andMathematical Statistics. Students achieving Credit or higher grades will berecommended for exemption from the professional examination. Exemptions fromprofessional actuarial examinations require above average performance in theequivalent University course.Students should have a solid background in mathematics and are assumed to be ableto use a computer to analyse financial problems. You should be able to use a wordprocessing package (such as WORD) and a spreadsheet (such as EXCEL).2.5 Student Learning OutcomesThe aims of Section 2.4 (A to D) have been broken down into the following learningoutcomes. At the end of the course students should be able to:A1. Explain the concepts of probability.A2. Explain the concepts of random variable, probability distribution,distribution function, expected value, variance and higher moments, andcalculate expected values and probabilities associated with thedistributions of random variables.A3. Define a probability generating function, a moment generating function,a cumulant generating function and cumulants, derive them in simplecases, and use them to evaluate moments.A4. Define basic discrete and continuous distributions, be able to apply themand simulate them in simple cases.A5. Explain the concepts of independence, jointly distributed randomvariables and conditional distributions, and use generating functions toestablish the distribution of linear combinations of independent randomvariables.A6. State the central limit theorem, and apply it.A7. Explain the concepts of conditional expectation and compounddistribution, and apply them.B1. Summarise the main features of a data set (exploratory data analysis).B2. Explain the concepts of random sampling, statistical inference andsampling distribution, and state and use basic sampling distributions.B3. Describe the main methods of estimation and the main properties ofestimators, and apply them.ACTL2002 – Probability & Statistics for ActuariesPage- 6

B4. Construct confidence intervals for unknown parameters.B5. Test hypotheses.B6. Investigate linear relationships between variables using correlationanalysis and regression analysis.B7. Explain the concepts of analysis of variance and use them.C1. Use R to implement the models introduced in the courseD1. Express his/her views on, and understanding of, an aspect of probabilityand statistics.These learning outcomes relate to the ASB Graduate Attributes in the following way:Course LearningOutcomesASB Graduate AttributesAll1. Critical thinking and problem solvingD12. CommunicationNone3. Teamwork and leadershipNone4. Social, ethical and global perspectivesC15. In-depth engagement with relevant disciplinary knowledgeC1 (All)6. Professional skills2.6 Coverage of IAAUST Learning OutcomesThis course corresponds largely with the actuarial professional subject CT3 Probabilityand Mathematical Statistics.The course’s Learning Outcomes relate to the aims of this Institute of Actuaries coursein the following way:Course Learning OutcomesInstitute of Actuaries aimsA1CT3: ii,A2CT3: iiiA3CT3: ivA4CT3: vA5CT3: viA6CT3: viiA7CT3: xivB1CT3: iB2CT3: viiiACTL2002 – Probability & Statistics for ActuariesPage- 7

B3CT3: ixB4CT3: xB5CT3: xiB6CT3: xiiB7CT3: xiiiC1NoneD1None3 LEARNING AND TEACHING ACTIVITIES3.1 Approach to Learning and Teaching in the CourseLectures will review the main topics and provide coverage of the course concepts.They are an opportunity for students to develop an understanding of the main topicscovered in the course and the level of knowledge expected. They provide a guide tothe course of study during the session and the material students need to read andreview. Students should read the prescribed readings prior to the lecture.Homework problem discussions and in-class activities are for students to ask questionson aspects of the course that need further clarification, and to interact with otherstudents in the course. Students need to attempt the homework problems alone firstand identify problems that require closer review. Students are strongly encouraged towork in teams as it is an opportunity to learn from other students and to develop teamskills.3.2 Learning Activities and Teaching StrategiesIt is expected the students will take a pro-active approach to learning. The course isorganised into learning activities given in the following table. The Course Aims andASB Graduate Attributes they should develop are also indicated.ActivityABCD123Required readingsXXXXXLectures and in-class activitiesXXXXXXXIn-class discussion of homeworkproblemsXXXXXXXOptional readingsXXXXOptional exercisesXXXX456XXXXXXXXXXXXXBy its nature, the actuarial program develops problem-solving and professional skills(ASB Graduate Attributes 1 and 6), and all activities contribute to that development.Thus, special care is taken when designing in-class activities, homework problems andoptional readings in order to also develop the ASB Graduate Attributes 2 to 5.ACTL2002 – Probability & Statistics for ActuariesPage- 8

Students are expected to perform these activities in the following time frame (for theoutcomes of week k):Week k-1Required readingsHave a first look at thehomework problems (ifpossible, in a team)Week kWeek k 1Attend lectureAttend in-class discussionof homework problems andreview solutionsAttempt homework problems(if possible, in a team), andprepare questionsReview lecture notes, andseek help if neededReview relevant pastquizzes and final examquestionsOptional readings andexercisesThus, you should, in a given week, work on these three different stages for theircorresponding three different course weeks. This proposed learning strategy should initself develop the 6th ASB Graduate Attribute. Thanks to the 12-weeks-in-13 model,homework problems are discussed in Week k 1.Detailed information about these activities for each week is available on Blackboard(see also the summary table at the end of this document).4 ASSESSMENT4.1 Formal RequirementsIn order to pass these courses, you must: achieve a composite mark of at least 50%; andmake a satisfactory attempt at all assessment tasks.Students who have an overall performance at the Credit level (65% and above) areeligible for exemption of the Institute of Actuaries CT3 examination.ACTL2002 – Probability & Statistics for ActuariesPage- 9

4.2 Assessment DetailsAssessment of your performance in the course will be done through a number of tasks.These are listed in the table below.Assessment TaskWeightLO23ASB GALengthDue DateQuiz10%Weeks 1-3:A1-A4, B11, 2, 5, 61 hour28 Mar(Monday, Week 5)2:00 p.m.–3:00 p.m.Tutorial Presentation5%D125 minutesN/AMajor Assignment15%A1-A7, B1,C1, D11, 2, 4, 5, 6NA16 May(Monday, Week11)11:00 a.m. sharpFinal examination70%All1, 2, 5, 62 hoursTBAIn-Class QuizTechnical skills are important in practice and this course provides foundation technicalskills that will be useful throughout your working life.In order to assess your understanding of the technical skills covered in the course therewill be a 1-hour quiz during the session. The quiz will be closed book. Students will onlybe allowed to bring the text "Formulae and Tables for Actuarial Examinations" into thequiz.Normal examination rules apply to the conduct of the quiz. Calculators will be allowedin the quiz and the final examination but a clear indication of all of the steps involved inyour calculations must be shown. The University will not supply calculators to studentsfor use in examinations where the provision of calculators has not been requested bythe course examiner. It is the student’s responsibility to be familiar with the rulesgoverning the conduct of examinations.The in-class quiz require written responses, with students earning marks for correctmathematical working as well as part marks for incorrect responses with correctmethod and reasoning. They test not only your knowledge of the material, but also thedepth of your understanding of it. They assist in the development of ASB GraduateAttributes 1, 5 and 6.An extensive collection of past quizzes is available on Blackboard.Tutorial PresentationThe aim of the tutorial presentations is principally to develop learning outcome D1. Italso aims specifically to develop ASB Graduate Attribute 2, as well as 1, 5 and 6. Youwill have another opportunity to make an oral presentation in the final year of youractuarial program.Tutorial presentations will be held in weeks 3 to 12. Each student is required to presentthe solution to an exercise in tutorials. A presentation can be a maximum of 5 minutesin length. Students will be allocated to a particular question in a particular week. Theseallocations will be made in advance and advised to students via Blackboard.Presentations will be marked out of five. The marking guide in use and other detailswill be posted on Blackboard.23Course Learning Outcome that is assessedASB Graduate Attribute that is assessedACTL2002 – Probability & Statistics for ActuariesPage- 10

AssignmentThere will be one assignment for this course. The assignment offers students theopportunity to engage in independent research, engage in critical analysis, selfreflection and problem-solving, as well as to demonstrate their understanding of theconcepts and perspectives that are central to actuarial studies. A solid attempt at theassignment will contribute towards developing ASB Graduate Attributes 1, 2, 5 and 6.The assignment will involve practical questions requiring statistical analysis using thesoftware package R, a written review of a statistical article and theoretical questions.The assignment questions, together with the marks allocated to all components of theassignment, will be made available to students on blackboard progressively. All detailswill be available by Friday 31 March 2011, at the latest.Students are reminded that the work they submit must be their own (see section 5below). While we have no problem with students working together on the assignmentproblems, the material students submit for assessment must be their own. This meansthat: The mathematical solutions you present are written up by you, withoutreference to any other student’s work.The statistical analysis you present is done by your own R code, which youyourself wrote and ran, without reference to any other student’s work.Any spreadsheet solutions you present are from your own spreadsheets, whichyou yourself developed, without any reference to any other student’s work.The analytic part of the assignment will be assessed on both technical accuracy andpractical application. The marking criteria for the article review will include: Summary of the key points in the articleClear outline of the arguments/analysis presentedEvidence of reflection on the article in terms of key issues, common themes andthe strengths and weaknesses of the author’s argument/approachConsistent, clear and well-supported argument/interpretation of the articleLogical structure, clear written expression, conform

Actuarial Studies: the director of Actuarial Programs (Dr. Bernard Wong bernard.wong@unsw.edu.au); Enrolment: ASB Student Centre. 2 COURSE DETAILS 2.1 Teaching Times and Locations This course will consist of three hours of lectures and a one hour tutorial per week. Lecture times and locations are as follows:

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