Probability and Statistics (확률 및 응용통계학)

Class Info Class Number: MATH 788-001 Dates: Mar 02 2022 - Jun 17 2022 Room: NS 318 Meeting time: Mon 10:30 - 11:50 (2B) Wed 9:00 - 10:20 (1A) Prof: Mark Siggers Office Hours Text:    `Introduction to Mathematical Statistics 7e' by Hogg McKean and Craig

Links Class Infomation Classnotes

Syllabus

We will cover chapters 1 through 4 of the text, and may add some applications to random graphs. The mathematical objectives are:

• Understand probability spaces and discrete and continuous random variables
• Computr basic expectations such as mean varience and moment generating functions.
• Transform multivariate distributions and find their marginal and conditional distributions.
• Become familiar with basic distributions; in particular poisson and normal distributions.
• Understand what a random experiment is, and be able to compute confidence intervals and set up a hypothesis test.

Here is an approximate schedule.

Week	Sections	Topics
1	1.1 - 1.4	Basics of probability
2	1.5 - 1.7	Random Variables
3	1.8 - 1.10	Expectation
4	2.1 - 2.2	Distributions of two random variables
5	2.3 - 2.5	Conditional Distributions
6	2.6 - 2.8	Several Random Variables
7	-	Test 1
8	3.1 - 3.2	Binomial and Poisson Distributions
9	3.3 - 3.4	Normal and related distributions
10	3.4, 4.1	Statistical Inference
11	4.1 - 4.3	Confidence intervals
12	4.4 - 4.5	Order statistics and hypothesis testing
13	4.6 - 4.9	Applications
14	buffer
15		Test 2

Class Format

The class will be standard lecture format with two tests. It will be in person.

Homework

There will be homework problems suggested each class. You do not have to submit them, but the test will draw largely from them, so you are strongly encouraged to do them.

Tests

There will be two tests. The dates will be decided about 2 weeks before the exams, but will fall within the departments suggested test weeks.

Evaluation

Attendence: 10%, Tests 2 x 45%. Attendence will be casually monitored unless attendence becomes too casual.