­­­­Mathematics

Statistics 564

Theory of Probability

Fall 2020

Course Syllabus

 

Course Homepage

 

session

date

slides/activity

videos

Homework

1

25Aug

Introduction

Introduction

2

27Aug

Axioms of Probability

Axioms of Probability

Homework 1 tex

3

1Sep

Counting

Counting

4

3Sep

Conditional Probability and Independence

Conditional Probability and Independence

Homework 2 tex

5

8Sep

Bayes Formula

Bayes Formula

6

10Sep

Random Variables and Distributions

Random Variables and Distributions

Homework 3 tex

7

15Sep

Mass Functions and Density Functions

Mass Functions and Density Functions

8

17Sep

Transformations

Transformations

Homework 4 tex

9

22Sep

Expected Values I

Expected Values I

10

24Sep

Expected Values II

Expected Values II

Homework 5 tex

11

29Sep

Functions of Random Variables

Functions of Random Variables

 

12

1Oct

Families of Random Variables I

Families of Random Variables I

Homework 6 tex

13

6Oct

Families of Random Variables II

Families of Random Variables II

 

14

8Oct

Exponential Families

Exponential Families

 

15

13Oct

Exam 1

 

 

16

15Oct

Probability Inequalities

Probability Inequalities

Homework 7 tex

17

20Oct

Joint and Marginal Distributions

Joint and Marginal Distributions

 

18

22Oct

Generating Functions and Conditional Expectation

Generating Functions and Conditional Expectation

Homework 8 tex

19

27Oct

Transformations I

Transformations I

20

29Oct

Transformations II

Transformations II

Homework 9 tex

21

3Nov

Covariance and Correlation I

Covariance and Correlation I

22

5Nov

Covariance and Correlation II

Covariance and Correlation IIa

Covariance and Correlation IIb

Homework 10 tex

23

8Nov

Order Statistics

Order Statistics

24

12Nov

t-Distribution

t-Distribution

Homework 11 tex

25

17Nov

Convergence Concepts

Convergence Concepts

 

26

19Nov

Monte Carlo Methods

Monte Carlo Methods

27

24Nov

Convergence in Distribution

Convergence in Distribution

 

28

1Dec

Central Limit Theorem I

Central Limit Theorem I

Homework 12 tex

29

3Dec

Exam 2

30

8Dec

Central Limit Theorem II

Central Limit Theorem II

Homework 13 tex

 

17Dec