Statistics for Economics (ECO 1400) Monsoon Semester 2023 Instructors: Faculty Name: Email Id: Office hours for students: Office Location: Teaching Assistants Name: Email Id: Office hours for students: Office Location: Pragya Jain pragya.jain@ashoka.edu.in To be announced To be announced To be announced To be announced To be announced To be announced Course Overview: This course is compulsory for all Economics Majors, PPE as well as Economics Minor. This course introduces students to the probability and statistical methods necessary for the study of economics at the undergraduate level. In particular, the course will cover random variables, probability distribution, joint probability distribution, interval estimation and hypothesis testing. Learning Outcomes: 1. The course will introduce students to the statistical method, viz., deducing the characteristics of a population from observing characteristics of a sample. The main objective of the course is to convey to the students why we need to understand statistics for scientific inference. 2. This will introduce students to the concept of random samples, random variables, their distributions which will be needed to move from properties of a sample to that of an underlying population. This will be preceded by a quick recap of probability theory. 3. The second half of the course will introduce students to methods of statistical inference, testing the significance of sample characteristics. Students will be given problem sets regularly throughout the semester for practice. Required Course Material: 1. Ross, Sheldon M.2004. "Introduction to Probability and Statistics for Engineers and Scientists", Third Edition, Elsevier Press. (Ross, henceforth) 2. Peck, Roxy, Olsen, Chris and Devore, Jay. 2012 "Introduction to Statistics and Data Analysis", Fourth Edition, Brooks/Cole Cengage Learning (POD, henceforth) 3. We will also refer to Ross, Sheldon. A First Course in Probability, 8th Edition. (Ross 2, henceforth) Other material, including online resources, might be introduced during the class, but those would be optional. Evaluation: Student grades have four components: final exam (50% weightage), first mid-term (20% weightage), second mid-term exam (20% weightage), and the total score in all problem sets combined (10% weightage). The final exam would be a 2-hour assessment on the entire syllabus. The syllabus for the first and second mid-term exams will be announced in class and on AMS. The instructor does not entertain marks obsession. Students should make use of office hours for any extra help or resources they require. The Ashoka grading scheme: A/A- letter grade = outstanding. Students know the mathematical techniques and have the ability to apply them in novel problems. B+/B/B- letter grade = good. Students have expertise in most of the mathematical techniques taught in the course. They may lack creativity in problem solving but are well trained to do well in any mathematical or applied course. C+/C/C- letter grade = adequate. Student knows enough. If s/he tries to revise the course content, s/he shall do well in any application of the course content. D+/D/D- letter grade = barely satisfactory. Student knows little. S/he requires guidance and then s/he would be able to apply the courses’ concepts. F letter grade = unsatisfactory. Student knows less than 40% of the course content. S/he has not achieved the minimum standards for this course. Course Rules: 1. The central objective of the course is to learn probability and statistics. To achieve this goal, we would solve innumerous problems and will frequently change the type of problems we encounter. In class, we will discuss problems with a difficulty of medium level. 2. Attendance policy: You can miss 8 classes over the semester with no penalty and no justification. If you miss 9 classes, you will be downgraded one grade (e.g., if your final grade was B, you would be given B-). If you miss 10 or more, you get an F. Attendance during mid-term exams and final exams is compulsory, no exam will be re-taken. 3. If students are late in entering the class by more than 5 minutes, they would be marked absent. Late assignments would not be graded. 4. Attending a class means sitting in the classroom for the full 90 minutes. Repeated entry and exit from the class will not be allowed. This means that once you exit the class before the class ends, you will not be allowed to re-enter and will be marked absent. 5. There is zero tolerance for accessing resource materials in final exams or during mid-term exams. If you are found cheating in any of the tests you will get an automatic F in the course. 6. Graphical calculators are not allowed but scientific calculators are allowed. Students shall not be allowed to share calculators in final exams or during class probes. Course map: This is an indicative schedule for 24 lectures. The actual distribution of lectures might deviate slightly depending on how fast or how slow we go in class. The total number of lecture meetings will be 26. The time for the remaining 2 lectures will be distributed over the semester to accommodate STATA instruction and spill overs from this indicated scheme LECTURE TITLE 1 -3 Backgrounder: Topics: Mean, Median, Mode, Percentiles, Variance, Standard Deviation, Graphs and Plots, Symmetry of graphs, Normal Distribution Correlation Coefficient Chebyshev’s Inequality 4 Combinatorial Analysis: The Basic Principle of Counting, Permutations, Combinations, Binomial Theorem (No Proof), Multinomial Coefficients 5 Probability: Sample Space and Events Axioms of Probability Some Simple Propositions (with Proofs) Sample Spaces having Equally Likely Outcomes BOOK POD: Chapter 1 Ross: Chapter 2 Ross 2: Chapter 1, Ross: Chapter 3 6-7 Conditional Probability and Independence: Conditional Probabilities Bayes’ Formula (with proofs) Independent Events Ross: Chapter 3 8-10 Random Variable: Discrete Random Variables, Properties of The Cumulative Distribution Mathematical Expectations Expected Value Expectation of a Function of a Random Variable Variance Expectation of Sums of Random Variables Chebyshev’s Theorem (No Proof) Ross: Chapters 4 All Proofs, wherever used. 11-12 Special Probability Distributions (Bernoulli, Binomial, Poisson are very important. All Proofs.) Ross: Chapter 5 13-14 Continuous Random Variables Special Probability Densities (Uniform, Normal, Exponential, Gamma are very important. All Proofs.) Ross: Chapter 5 POD: Chapter 7 https://onlinecourses.science.psu.edu/stat414/node/88 15 Functions of One Random Variable. (Very Important) POD: Chapter 9 16 Sampling Distribution (Complete Chapter) Only Proofs done in Class Ross: Chapter 6 17-20 Interval Estimation (Complete Chapter. Very Important). https://onlinecourses.science.psu.edu/stat414/node/194 Ross: Chapter 7 21 Point Estimation (may be shortened) Unbiased Estimators Efficiency Just state: Method of Moments, Method of Maximum Likelihood, Bayesian Estimation (Ideas Only) Ross: Chapter 7 22 Hypothesis Testing (Testing a Statistical Hypothesis) Ross: Chapter 8 POD: Chapter 10 23-24 Hypothesis Testing, Testing of Hypothesis including Mean, Variances and Proportions Topics (1-5) Ross: Chapter 8 POD: Chapter 10 Exam week: check Ashoka academic calendar for exact dates How to Succeed in This Class: Read before lecture. Set aside time before class to read the section of the book covered in lecture. Do lots of problems. You will need a lot of repetition to get these techniques down. If you have the time, I would encourage you to do extra problems from the book. • Work together. The best way to learn something is by explaining it to others. Your classmates can help you refine your understanding of the subject. • Come to office hours or make an appointment. If you have any difficulty with the homework, or if you have any questions about the material, please don’t hesitate to come to office hours. (This document was last updated on 20th July 2023)
