STAT 400 Probability and Statistics 1 Instructor: SHIWEI LAN shiwei@illinois.edu

Today’s Agenda Introduction Course Syllabus Introduction to Probability and Statistics

Instructor & TA Instructor TA Shiwei Lan (shiwei@illinois.edu) Office: Illini Hall 103C Office HR: M & W 2:00-3:00, or by appointment TA Teng Wu (CD1/3) (tengwu2@illinois.edu) Ying Liu (CD2/4) (yingl7@illinois.edu)

Course Outline Part 1 Part 2 Part 3 Probability Theory Statistics and Estimation Part 3 Hypothesis Testing

Course Format Three lectures (MWF) / Week Four Discussions / Week (Nearly) Weekly Homework Two In-Class Exams Final Exam (Cumulative)

Course Information Prerequisites: Course Website: Calculus 3 Course Website: Compass Homework: (Due on Friday 11:59PM) Lon-Capa

Course Textbook Probability and Statistical Inference, 9th Edition Hogg, Tanis and Zimmerman Class Examples and Reading Assignments will be from the textbook.

Course Grading Attendance Homework Midterms Final Course Total 50 (11-1) x 10 100 Midterms 100 x 2 200 Final 150 x 1 150 Course Total 500

Grading Scale A+ TBD A 93% A- 90% B+ 87% B 83% B- 80% C+ 77% C 73% C- 70% D+ 67% D 63% D- 60%

Homework Every (non-exam) week. (Except this week.) Posted, Electronically Submitted, and graded through COMPASS2g/LON-CAPA. Due: Each Friday, 11:59pm. 11 total, the lowest scores will be dropped. 10 Points each, Total of 100 Points.

Exams Two In-class midterms, 100 points each Three hour, cumulative final exam, 150 points The following will be allowed: Cheat sheet (1-2 pages, both sides) Calculator (Combination should be calculable)

Important Dates Exam 1: Monday, 02/25 Exam 2: Monday, 04/15 Final Exam: TBD

Schedule (Tentative) Dates Chapter Topics Week 1 1/14, 16, 18 1.1, 1.3   Dates Chapter Topics Week 1 1/14, 16, 18 1.1, 1.3 Introduction, Conditional Probability Week 2 1/23, 25 1.4. 1.5 Bayes Theorem, Independence Week 3 1/28, 30, 2/1 1.2, 2.1,2.2,2.3 Counting, Discrete R.V. Week 4 2/4, 6, 8 2.3, 2.4 Discrete distributions Week 5 2/11, 13, 15 2.5, 2.6, 3.1 Discrete distributions, Continuous R.V.

Schedule (Tentative) Dates Chapter Topics Week 6 2/18, 20, 22 3.1, 3.2   Dates Chapter Topics Week 6 2/18, 20, 22 3.1, 3.2 Continuous distributions Week 7 2/25, 27, 3/1 3.2, 3.3, 4.1 Week 8 3/4, 6, 8 4.1, 4.2, 4.4, 5.3 Bivariate distributions Week 9 3/11, 13, 15 5.6, 5.7, 5.8 CLT, Normal Approximation, Chebyshev Week 10 3/18, 20, 22 NO CLASS

Schedule (Tentative) Dates Chapter Topics Week 11 3/25, 27, 29 6.4   Dates Chapter Topics Week 11 3/25, 27, 29 6.4 Point Estimation, MLE, Method of moments Week 12 4/1, 3, 5 7.1, 7.4, 5.5 Confidence interval, sample size, t dist. Week 13 4/8, 10, 12 7.2, 7.3, 8.1 Confidence interval, Hypothesis test Week 14 4/15, 17, 19 8.1, 8,2 Hypothesis tests for mean / variance Week 15 4/22, 24, 26 8.2, 8.3, 9.2 Hypothesis tests for two proportions/ means Week 16 4/29, 5/1 9.2, Review Chi square test

Relationship between Probability and Inferential Statistics Population Sample The relationship btw the two disciplies can be summarized by saying tha tprob. Reasons form the population to the sample (deductive reasoning), and inferential statistics reasons from the sample to the population (inductive reasoning) Before we can understand what a particular sample can tell us about the pop, we should first understand the uncertainty assoc. with taking a sample from a given pop; Statistics

Statistics Characteristics of a sample are available to the experimenter. This information enables the experimenter to draw conclusion about the population.

Probability Properties of the population under study are assumed known. Questions regarding a sample taken from the population are posed and answered.

Set Theory

Terminology Random Experiment Outcome Set Outcome Space Empty Set Subset Event Complement

Terminology Random Experiment: an action whose outcome cannot be predicted with certainty beforehand (Ex: drawing a card, rolling a die, flipping a coin, …) Outcome: One specific result from a random experiment

Terminology Set: a collection/group of outcomes Usually abbreviated by a letter (A, B, etc.) Outcomes in a set are listed out separated by commas and encloses in curly braces. Example: A = {1, 3, 5} Subset: A set which has all its elements contained in another set Set A is a subset of Set B: A ⊂ B Ex: Queen of Hearts ⊂ Queens ⊂ Face Cards

Terminology Outcome Space (S): the set of all possible outcomes for a random experiment Event: any subset (containing ≥1 outcome) of S “Event” is more specific to Random Experiments, while “Subset” is the general mathematics term. In this class, the two terms tend to be used fairly interchangeably, since we almost exclusively discuss random experiments.

Reading Assignments This week Wed: Ch. 1.1: Properties of Probability Fri: Ch. 1.3: Conditional Probability