Textbook: Mathematical Statistics with Applications (7th ed.), by Dennis Wackerly, William Mendenhall III, Richard Scheaffer.

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1 ECON 502 Economic Statistics Section M1, TR 8:00-9:50 am, 215 David Kinley Hall Section M2, TR 1:30-3:20 pm, 119 David Kinley Hall Department of Economics UIUC Course Syllabus Fall 2015 Compass site login page: Instructor: Ali Toossi Office: 205C DKH Phone: Office hours: MW 11:00-12:00 or by appointment Assistant Instructor: Ruchi Singh Office: 205 DKH Phone: Office hours: MW:2:30-3:30 pm; TR:11:00-Noon Weekly Sessions: Section M1: Fridays 8:00-9:20am Room 215 David Kinley Hall Section M2: Fridays 9:30-10:50 am Room 119 David Kinley Hall The first meeting will be on Friday August 28. The Assistant Instructor will meet with you once a week on Fridays. These meetings will provide you with an opportunity to review the material covered in class and to work examples concerning the class. This course is designed to teach you what statistics mean and how to use statistics effectively in your own work and life. The text provides very good coverage of needed material. I will try to make effective use of the computer. The computer will serve several different purposes. It will be employed as a tool to understand and describe data sets, to compute statistical estimates and make inferences from data and finally, the computer will help understanding of theoretical concepts by allowing us to see how those concepts work. Textbook: Mathematical Statistics with Applications (7th ed.), by Dennis Wackerly, William Mendenhall III, Richard Scheaffer. Note that an ebook option is available which is cheaper than the textbook. Go to:

2 Attendance: You are required to attend both the lectures during the week and the recitation on Fridays. For excused absences, the student must provide an explanation and supply supporting evidence. Homework: There will be a required homework assignment approximately every two weeks (7-8 homeworks). In some of the problems assigned you have to use APPLETS (a short computer application especially for performing a simple specific task). You can access the APPLETS in the following site: nenumber=17 Exams: The class will have 4 quizzes, a midterm and a final examination. Quiz: There will 4 quizzes quizzes on: September 17, October 6 and November 3 and November 19. The dates might change. The quizzes will be one hour long in the first hour of the class. New lecture will be given in the second hour. Midterm: Tuesday, October 13, 7:00-9:00 pm in room 213 Gregory Hall Review Session: Monday, October 12, 6:00 pm in room 213 Gregory Hall Final: Regular Exam: Wednesday December 16 1:30-4:30 pm room 2 Education Conflict Exam: Friday December 11 1:30-4:30 pm room 215 DKH Grading: The course grade will be determined as follows: Class participation, instructor's judgment, and homework: 15% Quizzes: 20% Midterm examination: 30% Final examination: 35% The average determined above will be adjusted to take into consideration the trend of your performance and grades. Academic Integrity: Violations of academic integrity as given in the Code of Policies and Regulations will be taken extremely seriously, and students found cheating in the course (or helping others to cheat) will be penalized according to the Code s guidelines.

3 The course outline lists the dates each topic will be covered. The dates are approximate & could change. Lecture Date Topics Covered 1 August 25 2 August 27 3 September 1 4 September 3 Chapter 1: What is statistics? Descriptive & Inferential Statistics Population or Process, Sample Experimental vs Observational Data, Sampling errors, Sampling methods Types of Data: Quantitative vs Qualitative Types of Data: Cross section, Time series, Panel Descriptive statistics: Quantiles, Chapter 1: What is statistics? (Continued) Descriptive statistics: Mean, Median, mode, trimmed mean, Variance, CV, Interquartile range, range, MAD, Empirical Rules, Skewness, Kurtosis, Normal probability plot, JB test for normality Chapter 2: Probability Set theory, random experiments, sample space (Discrete, Continuous); event (simple, compound) Def. of probability=> 3 approaches: 1-probability As proportion of desired to possible outcomes, 2- probability as relative frequency, 3- axiomatic approach, Using axiomatic approach to derive some results Chapter 2: Probability (Continued) Assigning probability of event: Sample point method Tools for counting sample point: multiplication rule, permutation, combination More examples on counting Tuesday September 8 First Homework Due 5 September 8 6 September 10 Chapter 2: Probability (Continued) Conditional probability Independence of events Multiplicative law of probability additive law of probability Calculating probability of event: event composition method Chapter 2: Probability (Continued) The law of total probability & Bayes rule

4 random sampling and random variable Random variable and its realization P(Y=y) Tuesday September 15 Second Homework Due 7 September 15 Discrete probability distribution expected value: mean, variance mean & variance of a function of a random variable Examples on expected value and variance Bernoulli experiment & related distributions Bernoulli Distribution Binomial Distribution Thursday September 17 Quiz 1 8 September 17 9 September September September October 1 Examples on Binomial Distribution Hyper Geometric Geometric Negative Binomial ; Poisson Poisson Moments around origin and about the mean Moment generating functions Tchebysheff's Theorem Chapter4: Continuous random variables Distribution function (CDF) Discrete Y: CDF STEP function (right Continuous) Continuous Y: CDF Continuous function Continuous Y : Probability Density Function Example on PDF & CDF Chapter4: Continuous random variables Expected value & Variance Distributions: Uniform, Normal, Gamma Friday October 2 Third Homework Due Tuesday October 6 Quiz 2 13 October 6 Chapter4: Continuous random variables

5 14 October 8 Monday October 12 Tuesday October October October 20 Relationship between Gamma & Poisson Gamma Special cases: Chi-square, Exponential Relationship between Exponential & Poisson Chapter4: Continuous random variables Examples on exponential Hazard function Beta Distribution MGF for continuous RV Tchebysheff's theorem for continuous RV Chapter 5: Multivariate PD (discrete) Joint and cumulative probability distribution Marginal & conditional probability distributions Independent random variables, Expected value of a function of random variables conditional expectations 4 th Homework Due (by 4:45 pm in Ruchi s Mailbox) Review Session 6:00 pm in room 213 Gregory Hall Midterm Exam 7:00-9:00 pm in room 213 Gregory Hall (NO CLASS) Chapter 5: Multivariate PD (discrete) Example on bivariate discrete distributions Covariance & Correlation Regression and correlation expected value and variance of a linear function Chapter 5: Multivariate PD Examples on expectation and variance of linear functions of RV Law of Large Numbers Chapter 5: Bivariate PD (continuous) Introduction to double integration Joint Distribution function & density function Marginal & conditional probability distributions Independent random variables Expected value of a function of random variables

6 17 October October October 29 Chapter 5: Bivariate probability distributions (continuous) Conditional expectations Bivariate normal Chapter 6: Functions of random variables (sections ) Functions of random variables: 3 methods Distribution function Method Chapter 6: Functions of random variables (sections ) Method of Transformations examples on distribution & transformation method Method of MGFs Chapter 7: Sampling distribution & the CLT Definition of statistic sampling distribution of sample mean (when population variance is known) sampling distribution of sample variance t-student distribution sampling distribution of sample mean (when population variance is unknown) F distribution Sampling distribution of ratio of two sample variances (from two populations) Friday October 30 Fifth Homework Due Tuesday November 3 Quiz 3 20 November 3 21 November 5 22 November 10 Chapter 7: Sampling distribution & the CLT Examples on Sampling Distributions Normal approximation to the binomial Central limit theorem Chapter 7: Sampling distribution & the CLT Examples on CLT Chapter 8: Estimation (sections 8.1 to 8.4) Point estimation, Estimators Properties: Bias, mean square error Chapter 9: More on point estimates, methods of estimation Relative efficiency Chapter 9: More on point estimates Cramer-Rao theorem (page 448) consistency sufficiency Minimum Variance Unbiased Estimators (MVUE)

7 23 November 12 Example on MVUE Common MVUE Chapter 9: methods of estimation Estimation methods: moments, maximum likelihood Tuesday November 17 Sixth Homework Due 24 November 17 Chapter 8 revisited Confidence intervals large sample cl for the mean and proportion Small sample confidence interval for the mean difference of means and variance Small sample confidence interval for the difference of means Small sample confidence interval for the variance Thursday November 19 Quiz 4 25 November 19 November Introduction to Hypothesis Testing How to construct RR Type I and Type II errors Alpha, beta and Power of tests Power function Thanksgiving Recess Tuesday December 1 7 th Homework Due 26 December 1 Neyman Pearson Lemma Uniformly Most Powerful Tests 27 December 3 28 December 8 Likelihood ratio tests large sample tests p-values Relationships between HT & CI Small sample tests HT concerning variances Wednesday December 9 8 th Homework Due Final Exam: Regular Conflict Wednesday December 16 1:30-4:30 pm room 2 Education Friday December 11 1:30-4:30 pm Room 215 DKH

STA 225: Introductory Statistics (CT)

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