Mathematics 477 Section 1

Fall 2006

Prof. Stephen Miller


Mathematical Theory of Probability

Meets TF2 at 9:50A-11:10  in Murray Hall room 114, on the College Avenue Campus


Course Information:

Midterm Exam #1

100 pts

Midterm Exam #2

100 pts

Homework and Quizzes

100 pts

Final Exam

200 pts



Total

500 pts


Syllabus:

Lecture

Date

Reading

Topics

1

9/5

1.1--1.5

Counting

2

9/8

1.6, 2.1--2.3

More Counting; Axioms of Probability

3

9/12

2.4--2.5

Inclusion/Exclusion; Equally Likely Outcomes

4

9/15

2.5

Examples; Stirling's Formula

5

9/19

3.1--3.3

Conditional Probability; Bayes' Formula

6

9/22

3.4

Independent Events

7

9/26

3.5

Repeated Independent Trials

8

9/29

4.1--4.3, 4.9

Random Variables, Distribution Functions and C.D.F.'s

9

10/3

4.4--4.6

Expectation and Variance of Discrete RV

10

10/6

4.7--4.8

Special Discrete RV's---Bern., Bin., Geom. Distributions

11

10/10

4.8

More Special RV's---Poisson, Neg. Bin., Hypergeom. d.f.'s

12

10/13

5.1, 5.2

Continuous RV's; Expectation and Variance

13
10/17
EXAM 1 --- Sections 1.1--4.9

14

10/20

5.3--5.5

Special Cts RV's---Uniform, Expon., Normal d.f.'s

15

10/24

5.4

Normal Approximation to Binomial RV's

16

10/27

5.6, 5.7

Gamma RV's; Functions of a RV

17

10/31

6.1

Several RV's; Joint Distributions

18

11/3

6.2

Independent RV's

19

11/7

6.3

Sums of Independent RV's

20

11/10

7.1, 7.2

Linearity of Expectation

21

11/14

7.3

Higher moments

22

11/17

6.4, 6.5

Conditional Distributions

23

11/22

7.4

Covariance and Correlation

 --- THANKSGIVING BREAK ---
24
11/28
EXAM 2 --- Sections 5.1--6.5 and 7.1--7.3

25

12/1

7.5

Conditional Expectation

26

12/5

8.1, 8.2

Markov and Chebyshev Inequalities; Weak Law of Large Numbers

27

12/8

8.3

Central Limit Theorem

28

12/12

Catch up and review

FINAL EXAM - Tuesday December 19th, 8-11 am (location TBA)


Homework:

Due
Problems
9/19
Chapter 1 Problems 15, 20, 28 and Theoretical Exercise 14ab
10/3
Chapter 3 Problems 19, 21, 31, 45, 62
10/3
Chapter 4 Problems 4, 17, 35, 43 and Theoretical Exercises 5
10/10
Chapter 4 Problems 58, 61, 69, 82 and Theoretical Exercises 10, 16
10/31
Chapter 5 Problems 2, 4, 22, 31, and 32
11/7
Chapter 6 Problems 9, 16, 18, 26, and 33
11/14
Chapter 6 Problem 15, TE #14; Chapter 7 Problems 3, 9, and 12
11/22
Chapter 6 Problems 42 and 43; Chapter 7 Problem 42, 43, and Theoretical Exercise 13.