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Math 4610.001: Spring 2015

Meets: MWF 10:00-10:50 in Matthews Hall, Room 109.

Instructor: Professor John Quintanilla

Main Office: GAB, Room 418-D

Office Phone: x4043

Secondary Office: Wooten Hall, Room 335

Secondary Office Phone: x4235

E-mail: jquintanilla@unt.edu

Web page: http://www.math.unt.edu/~johnq/Courses/2015spring/4610/

Office Hours:

•           Wooten Hall office: Wednesdays 8:30-9:30 and Fridays 8-9:30

•           Main GAB office: Tuesdays 10-12, Thursdays 10-12, or by appointment. I'm fairly easy to find, and you're welcome to drop by outside of office hours without an appointment. However, there will be occasions when I'll be busy, and I may ask you to wait or come back later.

Required Text: Probability, by J. Pitman.

Strongly Recommended: Lecture notes for the semester are available for approximately $18. The Eagle Images Print Center is in room 124 of the University Service Building (USB), which located near the Fouts Field Parking Lot. This is not a convenient location, but offering them for sale elsewhere would increased the price of the lecture notes significantly. The Mean Green (stop 7 on the map) and Campus Cruiser shuttles both stop at USB. You should enter through the north door (that is, the door that isn’t facing Fouts Field) to easily get to the Print Center.

Course Description: Combinatorial analysis, probability, conditional probability, independence, random variables, expectation, generating functions and limit theorems.

Prerequisite: Math 2730.

Note: Math 3680 will become a prerequisite for Math 4610 in Fall 2015, but it’s not a prerequisite for this semester. That said, I realize that a large majority of students enrolled in Math 4610 have already taken Math 3680. For this reason, I will not spend much time in class motivating introductory concepts of probability found in Math 3680 and/or the middle-school and high-school TEKS. Instead, I’ll be assuming these introductory concepts as background knowledge which we will review through problem-solving during the first three weeks of the semester.

I have made certain videos from my Math 3680 class available on Blackboard for anyone who’d like a more thorough discussion or review of these concepts. The notes for these videos are part of the lecture notes available at the Eagle Images Print Center.

Actuarial Exams: Math 4610 should provide good preparation from the 1/P actuarial exam. More about the actuarial profession can be found at http://www.beanactuary.org, including extensive preparation for the 1/P exam that can also serve as review material for this course.

Course Topics

The following chapters and sections of the textbook will be covered according to the projected schedule below. Dates may change as events warrant.

  • Chapter 1: Introduction
    • 1.1 Equally Likely Outcomes
    • 1.2 Interpretations
    • 1.3 Distributions
    • 1.4 Conditional Probability and Independence
    • 1.5 Bayes' Rule
    • 1.6 Sequences of Events
  • Chapter 2: Repeated Trials and Sampling
    • 2.1 The Binomial Distribution
    • 2.2 Normal Approximation: Method
    • 2.4 Poisson Approximation
    • 2.5 Random Sampling
  • Chapter 3: Random Variables
    • 3.1 Introduction
    • 3.2 Expectation
    • 3.3 Standard Deviation and Normal Approximation
    • 3.4 Discrete Distributions
    • 3.5 The Poisson Distribution
  • Chapter 4: Continuous Distributions
    • 4.1 Probability Densities
    • 4.2 Exponential and Gamma Distributions
    • 4.4 Change of Variable
    • 4.5 Cumulative Distribution Functions
    • 4.6 Order Statistics
  • Chapter 5: Continuous Joint Distributions
    • 5.1 Uniform Distributions
    • 5.2 Densities
    • 5.3 Independent Normal Variables
    • 5.4 Operations
  • Chapter 6: Dependence
    • 6.1 Conditional Distributions: Discrete Case
    • 6.2 Conditional Expectation: Discrete Case
    • 6.3 Conditioning: Density Case
    • 6.4 Covariance and Correlation
    • 6.5 Bivariate Normal

 

January 21:

Review of Chapters 1-2

January 23:

Review of Chapters 1-2

January 26:

Review of Chapters 1-2

January 28:

Review of Chapters 1-2

January 30:

Review of Chapters 1-2

February 2:

Review of Chapters 1-2

February 4:

Review of Chapters 1-2

February 6:

Review of Chapters 1-2

February 9:

2.4

February 11:

3.1

February 13:

3.2

February 16:

3.2, 3.3

February 18:

3.3

February 20:

EXAM #1

Sage Hall Testing Center

 

Review #1

 

These videos give the solutions to each of the review exercises. I encourage you to attempt each problem on your own before watching the videos.

February 23:

3.3

February 25:

3.4

February 27:

3.4, 3.5

March 2:

3.5

March 4:

4.1

March 6:

4.1, 4.2

March 9:

4.2

March 11:

4.2

March 13:

4.4

 

SPRING BREAK

 

March 23:

4.5

March 25:

4.5, 4.6

March 27:

EXAM #2

Sage Hall Testing Center

 

Review #2

 

These videos give the solutions to each of the review exercises. I encourage you to attempt each problem on your own before watching the videos.

March 30:

4.6

April 1:

Moment-generating function

April 3:

Moment-generating function

April 6:

5.1, 5.2

April 8:

5.2

April 10:

5.3

April 13:

5.4

April 15:

5.4

April 17:

6.1

April 20:

6.2

April 22:

6.3

April 24:

EXAM #3

Sage Hall Testing Center

April 27:

6.3

April 29:

6.4

May 1:

6.4

May 4:

6.4, 6.5

May 6:

6.5

May 8:

READING DAY

Saturday, May 9:

FINAL, 8-10 am

Student Responsibilities

Grading Policies

The following schedule is tentative and is subject to capricious changes in case of extracurricular events deemed sufficiently important to the upper administration.

Final Exam

Saturday, May 9

8-10 am

24%

Exam 1

c. Week 5

19%

Exam 2

c. Week 9

19%

Exam 3

c. Week 14

19%

Homework

19%

A

90% and above

B

80% and below 90%

C

70% and below 80%

D

60% and below 70%

F

below 60%

Cooperation is encouraged in doing the homework assignments. However, cheating will not be tolerated on the exams. If you are caught cheating, you will be subject to any penalty the instructor deems appropriate, up to and including an automatic F for the course.

Attendance is not required for this class. However, you will be responsible for everything that I cover in class, even if you are absent. It is my experience that students who skip class frequently make poorer grades than students who attend class regularly. You should consider this if you don't think you'll be able to wake up in time for class consistently.

The grade of "I" is designed for students who are unable to complete work in a course but who are currently passing the course. The guidelines are clearly spelled out in the Student Handbook. Before you ask, you should read these requirements.

Exam Policies

Homework Policies

Final Note

In compliance with the Americans with Disabilities Act, I mention the following: It is the responsibility of students with certified disabilities to provide the instructor with appropriate documentation from the Dean of Students Office.

| Home || E-mail || Homework |
| Prof. Quintanilla || Department of Mathematics || University of North Texas |