Instructor Room No. Office Hours Email Lahore University of Management Sciences DISC 203 Probability and Statistics Fall Semester 2017 Muhammad Ali Raja 421 SDSB Building TBA ali.raja@lums.edu.pk Telephone 042 35608469 Secretary TA Office Hours Course URL (if any) Sec: Abdul Basit TA: TBA TBA http://suraj.lums.edu.pk/~ro/ COURSE BASICS Credit Hours 3 Lecture(s) Nbr of Lec(s) Per Week 2 Duration 75 minutes Recitation/Lab (per week) Nbr of Lec(s) Per Week Duration Tutorial (per week) Nbr of Lec(s) Per Week Duration COURSE DISTRIBUTION Core Elective Open for Student Category Yes Sophomore Close for Student Category COURSE DESCRIPTION This course is designed to provide students majoring in management and finance with an elementary introduction to probability and statistics with applications. Both descriptive and inferential statistics are covered. We first review techniques for organizing and presenting the raw data and elementary probability theory. Next, we discuss various techniques to make inferences. Along with probability theory, sampling distribution and central limit theorem shall be discussed. The idea of central limit theorem will naturally lead towards the confidence intervals and hypothesis tests for mean and proportion. We follow this discussion with single and multiple regression analysis, model building, design of experiments and categorical data analysis. The course also aims to give a hands on experience with using a statistical package R for carrying out data analysis. The main objective of the course is to provide students with the foundations of statistical inference mostly used in business and economics. COURSE PREREQUISITE(S) MATH 101 Calculus I COURSE LEARNING OBJECTIVES (CLO) 1. To enable students to solve problems using basic concepts of probability 2. To introduce students to the theory of inferential statistics To enable students to analyze data by identifying appropriate statistical techniques, computing statistics and 3. interpreting results To enable students to use R for statistical analysis of data 4. 5. To enable students to present and defend their empirical analysis effectively
LEARNING OUTCOMES (LO) 1. By the end of the course, students should be able to: summarize the data in a useful and informative manner 2. Use the basic concepts of probability and random variables explain the concept of the sampling distribution of static, and describe the behavior of the sample mean describe the foundations of classical inference involving confidence intervals and hypothesis testing and apply inferential methods Apply modeling techniques in simple and multiple linear regression analysis 3. Discuss critical elements in the design of a sampling experiment and analyze designed experiments using analysis of 4. variance analyze count data with two or more categories use R for statistical analysis of data defend their empirical analysis effectively, both in oral and written forms 5. GRADING BREAKUP AND POLICY NOTE: 5% marks will be adjusted in one of the components per instructor s judgement. It will be communicated in class. Quizzes (unannounced): 25% (No make up quiz) Midterm Examination: 25% Project: 10% (to be completed in groups number of students in a group TBA) CP/Attendance 5% Final Examination: 30% UNDERGRADUATE PROGRAM LEARNING GOALS & OBJECTIVES General Learning Goals & Objectives Goal 1 Effective Written and Oral Communication Objective: Students will demonstrate effective writing and oral communication skills Goal 2 Ethical Understanding and Reasoning Objective: Students will demonstrate that they are able to identify and address ethical issues in an organizational context. Goal 3 Analytical Thinking and Problem Solving Skills Objective: Students will demonstrate that they are able to identify key problems and generate viable solutions. Goal 4 Application of Information Technology Objective: Students will demonstrate that they are able to use current technologies in business and management context. Goal 5 Teamwork in Diverse and Multicultural Environments Objective: Students will demonstrate that they are able to work effectively in diverse environments. Goal 6 Understanding Organizational Ecosystems Objective: Students will demonstrate that they have an understanding of Economic, Political, Regulatory, Legal, Technological, and Social environment of organizations. Major Specific Learning Goals & Objectives Goal 7 (a) Program Specific Knowledge and Understanding Objective: Students will demonstrate knowledge of key business disciplines and how they interact including application to real world situations. Goal 7 (b) Understanding the science behind the decision making process (for MGS Majors) Objective: Students will demonstrate ability to analyze a business problem, design and apply appropriate decision support tools, interpret results and make meaningful recommendations to support the decision maker
Indicate below how the course learning objectives specifically relate to any program learning goals and objectives PROGRAM LEARNING GOALS AND COURSE LEARNING OBJECTIVES COURSE ASSESSMENT ITEM OBJECTIVES Goal 1 Effective Written and Oral Students get a number of opportunities to Project and Exams Communication demonstrate their ability to communicate effectively (CLO # 5) Goal 2 Ethical Understanding and Students demonstrate an honest reporting Project and use of data (CLO #5) Reasoning Goal 3 Analytical Thinking and Problem This is an important objective of the Quizzes, Project and Exams course (CLO # 1,3,5) Solving Skills Goal 4 Application of Information Students learn to use R for data analysis Project (CLO # 4) Technology Goal 5 Teamwork in Diverse and Students work in groups on the project Project Multicultural Environments Goal 6 Understanding Organizational NA NA Ecosystems Goal 7 (a) Discipline Specific Knowledge Comprehensive coverage of topics in Quizzes, HW, Project and Exams elementary probability and statistics and Understanding (CLO # 1 5 & LO # 1 9) Goal 7 (b) Understanding the science behind the decision making process Students apply appropriate statistical Quizzes, HW, Project and Exams methods to answer data based decision problems (CLO # 1 5) EXAMINATION DETAIL Yes/No: Yes Combine Separate: Combine Midterm Duration: 100 minutes Exam Preferred Date: Exam Specifications: closed book, closed notes, help sheet allowed (A4 size, single sided, hand written), calculators Allowed Final Exam Yes/No: Yes Combine Separate: Combine Duration: 100 minutes Exam Specifications: closed book, closed notes, help sheet allowed (A4 size, two sided, hand written), calculators Allowed
COURSE OVERVIEW RECOMMENDED LECTURE TOPICS OBJECTIVES READINGS Introduction: Statistics, Data and Statistical Chapter 1 Course introduction 1 Thinking Understand the nature and scope of Statistics 2 3 Methods of Describing Sets of Data Chapter 2 Choose a suitable way of Graphical Methods; Summation Notation; Central presenting raw Statistical Data Tendency; Variability; Relative Standing; Standard Calculate and interpret measures Deviation of central tendency and variability 4 Lab Session Describe data using R Probability Chapter 3 Describe the sample space Events, Sample Spaces and Probability; Unions and Compute probabilities Intersections; Complementary Events; The Understand the notion of Random Additive Rule and Sampling Mutually Exclusive Events; Conditional 5 6 Probability; The Multiplicative Rule and Independent Events; Random Sampling; Bayes Rule Random Variables and Probability probabilities for distributions Distributions over discrete sets Discrete Random Variables: Probability Chapter 4 Calculate the mean and variance of Distributions for a discrete random variable Discrete Random Variables; Expected Values of Recognize cases where Binomial Discrete Distribution could be an Random Variables; The Binomial Random appropriate model; compute Variable; The probabilities for a Binomial Poisson Random Variable Distribution and approximate Continuous Random Variables: Probability Binomial probabilities using a Distributions for Chapter 5 Normal Distribution; Find Continuous Random Variables; The Uniform probabilities for continuous Distribution; distributions The Normal Distribution; The Exponential Use the key properties of the Distribution Normal Distributions Sampling Distributions: The Concept of Sampling Recognize cases where Distributions; Properties of Sampling Distributions; Poisson,
The Sampling Distribution of the Sample Mean Uniform and Exponential Distributions could be appropriate and compute corresponding Probabilities 7 10 Describe properties of the sampling distribution of sample mean Understand and apply Central Limit Theorem 11 13 14 Inference Based on a Single Sample: Estimation with Confidence Intervals Large Sample Confidence interval for a Population Mean; Small Sample Confidence Interval for a Population Mean; Large Sample Confidence Interval for a Population Proportion; Determining the sample size; Sample Survey Designs Tests of Hypothesis The Elements of a Test of Hypothesis; Large Sample Test of Hypothesis About a Population Mean; Small Sample Test of Hypothesis About a Population Mean; Large Sample Test of Hypothesis About a Population Proportion; Observed Significance Levels: p values Midterm Exam Chapter 6 Chapter 7 Calculate and interpret Confidence Intervals and Confidence Levels Remember steps in Classical Hypothesis testing Describe Type I and Type II Errors Conduct Tests of Hypothesis according to a given situation and Interpret the results. 15 16 17 19 Inference Based on Two Samples Chapter 8 Apply Classical Hypothesis Testing Comparing Two Population Means: Independent to compare two populations and Sampling; Comparing Two Population Means: draw inference Paired Difference Experiments; Comparing Two Population Proportions: Independent Sampling; Determining the Sample Size; Comparing Two Population Variances: Independent Sampling Simple Linear Regression Chapter 11 Define the concept of least squares Probabilistic Models; Fitting the Model: The Least estimation in linear regression Squares Approach; Model Assumptions; Assessing Explain why correlation need not
20 Lahore University of Management Sciences the Utility of the Model: Making Inference about necessarily imply causation the Slope; The Coefficients of Correlation and Evaluate the fit of a linear model Determination; Using the Conduct inference for the slope Model for Estimation and Prediction and intercept parameters Lab session Use R for linear regression Multiple Regression and Model Building (Lectures Chapter 12 Define the concept of Least and R demonstrations) Squares Multiple Regression Regression in Multiple Regression Test the utility of a Multiple 21 22 Multiple Regression: The Model and the Regression Model and use it for Procedure; estimation and prediction The Least Squares Approach; Model assumptions; Interpret the results of a Multiple Inference Regression Model and draw About the Slope Parameters; R 2 and the Analysis of inference Variance F Test; Using the Model for Estimation Understand how to select a model and Prediction that is appropriate for given data Use R for Multiple Regression Model Building Analysis 23 25 The Two Types of Independent Variables: Quantitative and Qualitative; Models with a Single Quantitative Independent Variable; Models with Two or More Quantitative Independent Variables; Testing Portions of a Model; Models with One Qualitative Independent Variable; Comparing the Slopes of Two or More Lines; Comparing Two or More Response Curves; Stepwise Regression Project Presentations 26 28 TEXTBOOK(S)/SUPPLEMENTARY READINGS Required Texts: TBA Supplementary: Gonick, L. and Smith W.,The Cartoon guide to Statistics, Harper Perennial, NY. Resources for R (statistical computing and graphics software): https://www.r project.org/, https://www.rstudio.com/