LAHORE SCHOOL OF ECONOMICS. Course information & Study Guide. Probability and Statistical Inference

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1 LAHORE SCHOOL OF ECONOMICS Course information & Study Guide Probability and Statistical Inference Course Instructor: Assistant Professor Azmat Nafees

2 CONTENTS Introduction Course overview Learning resources Assessment Course calendar Appendix This Course information needs to be read in conjunction with Extra course information available at: INTRODUCTION WELCOME Welcome to this course on Probability and Statistical Inference. In the next fourteen weeks, we will study the role of Probability and application of Statistical Inference in business and management, and consider how probability distributions can be a source of sustainable competitive advantage for organisations. The class activities will be facilitated by me, but I hope you will actively participate and guide your own learning. I look forward to an engaging and stimulating study period for all of us! Azmat Nafees Course Instructor Office Hours: Friday 11:00 13:00 Location: Office: H2-10, Burki Campus azmatn@lahoreschool.edu.pk Telephone: (0423) Ext. 260 Course homepage: SCHOOL CONTACT DETAILS Lahore School of Economics Burki Campus Department of Mathematics and Statistical Sciences Lahore 2

3 COURSE OVERVIEW COURSE AIM The primary goal of this course is to teach various probability distributions applied in business and economics field. The course is also designed to provide a clear introduction to philosophy of statistical inference. It will provide a sound, intuitive understanding of the basic concepts with complete understanding of research and analysis. COURSE STATEMENT/ TEACHING STRATEGY Teaching is made up of lectures, exercises and computer experiments. To achieve the desired objectives of teaching probability and inference there will be a balanced mixture of theory, methods and applications. The course mainly comprises of covering probability distributions, hypothesis, parametric and non-parametric tests. The students will have to submit take home assignments based on some probability distributions and various analytical tests. Extensive exercises for class assignments and computer exercises will be given during discussion session. Students performance will be evaluated based on class assignments, exams and software application. PREREQUISITE(S)/ ASSUMED KNOWLEDGE Good knowledge and understanding of Calculus, Statistics I and Basic Probability. TEACHING AND LEARNING ARRANGEMENTS This course is taught in a lecture and seminar format. UNIT VALUE OF COURSE 4 credit hours GRADUATE GRADING CRITERIA The following table shows the Lahore School of Economics Graduate Grading Criteria applied to assessment in this course: No. A Grade Value 80% and above A- 75% % B+ 70% % B 65% % B- 60% % C+ 56% % C 52% % C- 48% % D 45% % F 44.99% or below 3

4 LEARNING RESOURCES TEXT You will need continual access to the following text in order to complete this course. The library will hold two copies of the nominated text books and therefore you will need to acquire the book. Irwin Miller & Marylees Miller 2004, Mathematical Statistics with Applications, 7 th Edition, Pearson Education MATERIALS TO BE ACCESSED ONLINE Lecture slides and discussion group from course homepage: Other core Readings Robert V Hogg & Elliot A. Tanis 2007, Probability and Statistical Inference, Pearson Education, 7 th ed. H J Larson, Introduction to Probability Theory and Statistical Inference, 4 th ed Lee J. Bain, Max Engelhardt 1992, Introduction to Probability and Mathematical Statistics, 2 nd Edition, Duxbury Thomson Learning Ernest F. Haeussler, Jr. & Richard S. Paul 1993, Introductory Mathematical Analysis for Business, Economics and Social & Life Sciences, 6 th Edition, McGraw Hill Croucher, John S. 2002, Introductory Mathematics and Statistics for Business, 4 th Edition (Reprinted 2003, 2004), McGraw Hill Amir D. Aczel 2009, Complete Business Statistics, 7 th Edition McGraw Hill 4

5 ASSESSMENT ASSESSMENT SUMMARY Form of assessment Weighting Due date Assignment 1 5% October 1, 2010, 2:00pm, Week 5 Assignment 2 7% October 29, 2010, 2:00pm, Week 9 Assessment 3 9% December 3, 2010, 2:00pm, Week 14 Quiz 1 (Lec 1 4) 3% September 16-18, 2010 Week 3 Quiz 2 (Lec 5 9) 3% October 4-6, 2010 Week 6 Quiz 3 (Lec 16 19) 3% November 8-10, 2010 Week 11 Quiz 4 (Lec 21 24) 3% Nov 29 Dec 1, 2010 Week 14 Class Assignments 4% CP or Attendance 5% Midterm Exam 20% Week 8 Final Exam 40% Week 16 * Best three quizzes will be selected ASSESSMENT DETAILS Details of assignment submission and return are listed under each assessment task. Assignments will be returned to you within two weeks of submission. All assignments must use the Assignment cover sheet (available in the Appendix of this document and in student portal under course material) whether submitted electronically or in hard copy. Late assignments that do not have approved extensions will incur penalties of 5% a day late. Assignments without approved extension will not be accepted a week after the due date. There is no opportunity for supplementary assessment in this course. Resubmissions, remarking and extensions may all be available subject to negotiation with the Course Instructor. Assignment 1 Numerical Questions (Concepts of Probability & Mathematical Expectations) In this assignment you are asked to compute the probabilities using properties. The purpose of this assignment is to develop the theoretical concepts of probability for different types of random variables. Specifically, the exercise aims to: 1. build knowledge of simple probability and its application 2. develop the concept of calculating mathematical expectations 5

6 3. understanding the importance of Bayes theorem and its application in business and economics 4. learning the concept of conditional and marginal probability distribution functions Assignment should be submitted either electronically using Student portal or in hand to course TA. Feedback on this assignment will be provided on the Student portal. Assignments will be returned within 10 working days. Assignment 2 Numerical Questions (Probability Distributions) In this assignment you are asked to apply the concepts of probability distributions that are required to infer about the various business conditions. The purpose of the assignment is to develop the concepts of describing the information using probability distributions after identifying the type of the variables. Specifically, the exercise aims to: 1. build knowledge of discrete probability distributions along with their applications 2. develop a concept of continuous probability distribution and their applications 3. understanding the importance of properties and application of the probability distributions Assignment should be submitted either electronically using portal or in hand to the course TA. Feedback on this assignment will be provided on the Student portal. Assignment will be returned within 10 working days. Assignments 3 Numerical Questions (Hypothesis Testing & Non-Parametric Tests) In this assignment you are asked to use the concepts of probability density functions that are required to calculate statistical values in order to test the hypothetical statements for the different types of parameters and non-parametric hypothesis that are required to infer about the various business conditions. The purpose of the assignment is to develop the concepts of describing the information using various parametric and non-parametric tests after identifying the type of the variables. Specifically, the exercise aims to: 1. build the knowledge of using probability distributions to test their estimated parameters 2. develop a hypothetical statement for the population parameters of a given random variable 3. understanding the importance of various parametric and non-parametric tests for hypothesis Assignment should be submitted either electronically using Student portal or in hand to course TA. Feedback on this assignment will be provided on the Student portal. Assignments will be returned within 10 working days. QUIZ 1 Topics that quiz 1 will cover are: basic concepts of probability, conditional probability, total probability and application of Bayes theorem, finding probability from probability density function (pdf), cumulative distribution functions (CDF), 6

7 QUIZ 2 Topics that quiz 2 will cover are: mathematical expectations (moments) for pdf and their applications, Conditional distribution for two continuous random variables, stochastic independence, Bernoulli distribution and Binomial distribution, Poisson distribution, Negative Binomial distribution and their applications QUIZ 3 Topics that quiz 3 will cover are: Gamma distribution and its applications, point estimation, Method of moments, maximum likelihood estimation, testing a statistical hypothesis, Type I error, Type II error. QUIZ 4 Topics that quiz 4 will cover are: Chi-square test, testing proportions and variances, ratio of variances, F-distribution, Non-parametric tests: Rank Correlation coefficient test, Sign test, Wilcoxon sign rank. VARIATIONS TO ASSESSMENT TASKS Students may request a variance to assessment methods, tasks and timelines based on medical or sympathetic observance grounds. Such variations must be requested within the first two weeks of the course (or equivalent for accelerated or intensive teaching). Alternative arrangements due to unexpected circumstances should be discussed with the Course Instructor as required. ACADEMIC INTEGRITY The university aims to foster and preserve the scholarly values of inquiry, experimentation, critical appraisal and integrity, and to foster these values in its students. Academic Integrity is a term used at university to describe honest behaviour as it relates to all academic work (for example papers written by staff, student assignments, conduct in exams, etc) and is the foundation of university life. One of the main principles is respecting other people s ideas and not claiming them as your own. Anyone found to have used another person s ideas without proper acknowledgement is guilty of Academic Misconduct and the University consider this to be a serious matter. The Lahore School of Economics wants its students to display academic integrity so that its degrees are earned honestly and are trusted and valued by its students and their employers. To ensure this happens and that students adhere to high standards of academic integrity and honesty at all times, the University has policies and procedures in place to promote academic integrity and manage academic misconduct for all students. 7

8 COURSE CALENDAR WINTER TERM 2009 Week 1 Aug 30 Sep 4 Lec 1 Lecture sessions Probability Models, Basic probability concept, Notations and terminologies in probability, types of events, Computing simples probability, and applications of probability properties Discussion sessions Discussion on specific topic 2 Conditional probability and Bayes theorem Week 2 Sep 6 Sep Discrete prob. distribution function, its probability density function (pdf), Continuous prob. distribution function, its probability mass function (pmf), Cumulative Distribution Function (CDF), Week 3 Sep 13 Sep Mathematical expectations, Conditional expectations, and variance Marginal distribution for discrete and continuous probability distribution Quiz 1 Week 4 Sep 20 Sep Conditional distribution for two continuous random variables, stochastic independence Bernoulli distribution and Binomial distribution, their applications Week 5 Sep 27 Oct Negative binomial distribution and Poisson distribution, their applications Hyper-geometric distribution, Geometric distribution, and their applications Submission of Assignment 1 October 1, 2010, 2:00pm Week 6 Oct 4 Oct 9 11 Multinomial distribution and its applications Quiz 2 12 Exponential distribution and its applications Week 7 Oct 11 Oct Normal distribution and its applications 14 Normal approximation to Binomial distribution, continuity correction factor and errors of approximation Week 8 15 Mid-Term Exam (Oct 18 Oct 23) Lec Lecture sessions Discussion sessions 8

9 Week 9 Oct 25 Oct 30 Week 10 Nov 1 Nov 6 16 Gamma distribution and its applications 17 Point estimation: Method of moments, Submission of Assignment 2 October 29, 2010, 2:00pm 18 Point estimation: Maximum likelihood estimation, 19 Hypothesis testing: testing a statistical hypothesis, Type I error, Type II error. Week 11 Nov 8 Nov Hypothesis testing: Testing means Hypothesis testing: testing proportions, Chi-square test Quiz 3 Week 12 Nov 15 Nov Hypothesis testing: testing variance, ratio of variances, F-distribution Non-parametric tests: Rank Correlation coefficient test Week 13 Nov 22 Nov Non-parametric tests: Sign test, Wilcoxon sign rank test Non-parametric tests: Rank sum U test Week 14 Nov 29 Dec 4 26 Non-parametric tests: Rank sum H test 27 Revision Quiz 4 Submission of Assignment 3 December 3, 2010, 2:00pm Week 15 Activity Week (Dec 6 Dec 11) Week Final Exam (Dec 13 Dec 18) 9

10 APPENDIX A LAHORE SCHOOL OF ECONOMICS Assignment Cover Sheet An Assignment cover sheet needs to be included with each assignment. Please complete all details clearly. If you are submitting the assignment on paper, please staple this sheet to the front of each assignment. If you are submitting the assignment online, please ensure this cover sheet is included at the start of your document. (This is preferable to a separate attachment.) Please check your Course Information Booklet for assignment submission locations. Name: Student ID Course code and title: Probability and Statistical Inference Program: BSC II Course Instructor: Assistant Professor Azmat Nafees Assignment number: Teaching Associate: Jawad Khalid Due date: Assignment topic as stated in Course Information Booklet: Further Information: (e.g. state if extension was granted and attach evidence of approval, Revised Submission Date) I declare that the work contained in this assignment is my own, except where acknowledgement of sources is made. I authorise the University to test any work submitted by me, using text comparison software, for instances of plagiarism. I understand this will involve the University or its contractor copying my work and storing it on a database to be used in future to test work submitted by others. Note: The attachment of this statement on any electronically submitted assignments will be deemed to have the same authority as a signed statement. Signed: Date: Date received from student Assessment/grade Assessed by: Recorded: Dispatched (if applicable): 10

S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y

Department of Mathematics, Statistics and Science College of Arts and Sciences Qatar University S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y A m e e n A l a