1. STAT 400 Probability and Statistics 1
Instructor: SHIWEI LAN

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

3. 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)
Ying Liu (CD2/4)

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

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

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

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

8. 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

9. 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%

10. 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.

11. 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)

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

13. 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
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.

14. 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

15. 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

16. 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

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

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

19. Set Theory

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

21. 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

22. 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

23. 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.

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