­­­­Mathematics

Statistics 564

Theory of Probability

Fall 2019

Course Syllabus

 

Course Homepage

 

session

date

slides/activity

videos

text pages

Homework

1

27Aug

Introduction

Introduction

Introduction

2

29Aug

Axioms of Probability

Axioms of Probability

1-12

Homework 1

3

3Sep

Counting

Counting

13-19

4

5Sep

Conditional Probability and Independence

Conditional Probability

20-26

Homework 2

5

10Sep

Bayes Formula

Bayes Formula

6

12Sep

Random Variables and Distributions

Random Variables and Distributions

27-33

Homework 3 tex

7

17Sep

Mass Functions and Density Functions

Mass Functions and Density Functions

8

19Sep

Transformations

Transformations

 

Homework 4 tex

9

24Sep

Expected Values I

Expected Values I

 

10

26Sep

Expected Values II

Expected Values II

 

Homework 5 tex

11

1Oct

Functions of Random Variables

Functions of Random Variables

 

 

12

3Oct

Families of Random Variables I

Families of Random Variables I

 

Homework 6 tex

13

8Oct

Families of Random Variables II

Families of Random Variables II

 

 

14

10Oct

Exponential Families

Exponential Families

 

 

15

15Oct

Exam 1

 

 

 

16

17Oct

Probability Inequalities

Probability Inequalities

 

Homework 7 tex

17

22Oct

Joint and Marginal Distributions

Joint and Marginal Distributions

 

 

18

24Oct

Generating Functions and Conditional Expectation

Generating Functions and Conditional Expectation

 

Homework 8 tex

19

29Oct

Transformations I

Transformations I

 

 

20

31Oct

Transformations II

Transformations II

 

Homework 9 tex

21

5Nov

Covariance and Correlation I

Covariance and Correlation I

 

 

22

7Nov

Covariance and Correlation II

Covariance and Correlation II

 

 

23

12Nov

Order Statistics

Order Statistics

 

Homework 10 tex

24

14Nov

t-Distribution

t-Distribution

 

 

25

19Nov

Convergence Concepts

Convergence Concepts

 

 

26

21Nov

Monte Carlo Methods

Monte Carlo Methods

 

Homework 11 tex

27

26Nov

Exam 2

 

 

 

28

3Dec

Convergence in Distribution

Convergence in Distribution

 

 

29

5Dec

Central Limit Theorem I

Central Limit Theorem I

 

Homework 12 tex

30

10Dec

Central Limit Theorem II

Central Limit Theorem II

 

 

 

17Dec

Final Exam