MA451 - Probability Theory (Fall 2009)

 

General Information:

Instructor: Dr. Laura McSweeney (lmcsweeney [at] fairfield.edu)

Meeting Times: Wednesdays  6:30 – 9pm, Room BNW 256

Text: Miller and Miller’s John E. Freund’s Mathematical Statistics, 7th Edition

Office Hours: Monday, Wednesday and Thursday 11a – noon, Wednesday 5– 6pm and by appointment in Bannow 111

                        (203)254-4000 x2194

Course Web site:  http://www.faculty.fairfield.edu/lmcsweeney/MA451.htm

 

Please purchase a binder for the course since you will get many handouts this semester.  I recommend that you bring a TI-83 Graphing calculator to each class.  This calculator has the statistical functions that we will use. We may also use Excel for some exploratory data analysis.

 

Course Calendar (updated weekly)

Tentative Semester Calendar

Solutions to Chapter 2.6 – 2.8 Examples (Bayes’ Rule)

 

Birthday Problem (Excel File)

Law of large Numbers (Excel File)

Results of Sum of Dice (Excel File)

 

Course Description:

This is a calculus-based probability theory course which will cover most of the material from Chapters 1 - 7 in the text.  The emphasis of the course will be on the rigorous development of the theories and main tools of probability.  There will be heavy emphasis on proofs as well as applications.  Differential and integral and calculus (as in MA 171, 172) will be used throughout the semester.  In addition, a minimal amount of multivariate calculus will be assumed. A follow-up course, MA 452, will be offered in the spring.

 

Student Learning Objectives: The student will be able to

1.  Apply counting techniques to solve problems in discrete probability.

2.  Prove and apply basic probability laws, theorems and properties.

3.  Understand the relationship between probability and cumulative distribution/density functions and understand the

            relationship between joint and marginal distribution/density functions.

4.  Derive and calculate probabilities, expectations and other properties of discrete and continuous random variables.

5.  Apply knowledge of certain basic families of random variables to solve problems.

 

Topics to be covered:

Interspersed in these chapters will be an introduction to data analysis.  We will use both the graphing calculator and Excel for these topics.  Excel is available at all on campus computer labs, including the library and BNW 124. 

 

Chapter 1:  Combinations, Permutations

 

Chapter 2:  Sample Spaces, Events, Probability, Conditional

Probability, Independent Events, Bayes' Theorem

 

Chapter 3:  Random Variables (RV), Probability Distribution/Density Functions, Joint

Distributions, Marginal Distributions, Conditional Distributions

 

Chapter 4:  Expected Value and Variance, Moment Generating Functions, Linear

Combinations of RV's

 

Chapter 5:  Discrete RV's (Uniform, Bernoulli, Binomial, Geometric, Neg. Binomial,

Hypergeometric, Poisson)

 

Chapter 6:  Continuous RV's (Uniform, Exponential, Gamma, Beta, Normal)

            Normal Approx. of Binomial

 

Chapter 7:  Functions of RV's (as time permits)

 

Note:  Students interested in the actuarial field and who plan to take the first actuary exam should feel comfortable with all the material in Chapters 1 – 7.  [Check out http://www.soa.org/ and http://www.beanactuary.com/ for more information about actuaries and the exam process.]

 

Grading:

·         Homework:  Homework problems will be given out every week and will be due two classes later at the beginning of class.  While I encourage you to work with each other and to ask me questions, all homework is to be written up individually.  All work should be done neatly.  To earn full credit you must include more than just a final numerical result. A brief summary of steps taken and concluding statement should be included.  Proofs should be written concisely and with justification for each step.  This may require you to write the proof many times to make it as concise as possible. Assignments will be given in class.

 

The grading scheme for homework problems usually follows this rubric:

10pts - Perfect solution with explanations and/or justifications

8 or 9 pts:  Nearly perfect solution with only minor mistakes     

            (minor arithmetic mistake, typo, “Oops!” mistakes)

7pts: Significant progress made toward correct solution but entire solution is not

                        complete or correct.

5pts:  Minor progress made toward correct solution or  

some of the questions were not answered (major algebraic mistake)

0pts:  No progress made towards a correct solution or no effort made

 

·         In-Class Activities:  These in-class group activities are designed to explore theories and concepts in more depth in a more relaxed setting and to get you involved.  Completing the activities should help you with the homework.

 

·         Articles: You will be asked to read research articles that cover the topics covered in class.  You will be required to work out all details of the article on your own and be able to verify/justify the details in the article (say on an exam). The goal of these assignments is to expose you to interesting applications and the research process.

 

·        Exams:  There will be two in-class exams during the semester, a midterm and final exam.  The questions asked on the exams will NOT always be “just like” homework questions.  I will be testing your understanding of the concepts learned in class and your ability to apply your knowledge to new situations.  The dates of the (in-class) exams are October 28th and December 16th.

 

 

Final Grade Calculation:

Assignment                                                                             Total Possible Points

Homework [your points/total possible pts * 100]                               100

Exams [100 points each]                                                                     200

-----------------------------------------------------------------------------------------------------

Total Points Possible                                                                           300

Your grade = Total Points Earned/300 *100%.

The usual grade ranges apply.  (ex:   80 £ x < 83  = B-,  83 £ x < 87 = B,  87£ x < 90, B+)

 

Attendance Policy and Missed Work:

Attendance to each class is expected since we will be covering new material in each class (approximately a half to one chapter per class).  Since the evening class is intensive, missing one class is equivalent to missing a week of a traditional class; and thus should be avoided. You are responsible for getting notes and assignments for any classes missed.  You can also check the course website to see what topics you missed.  Remember that lack of attendance is often an indicator of whether a student succeeds in a course or not.  Please note that if you miss an exam, you are not guaranteed or entitled to a make-up exam (Student handbook 2008-2009 edition, pg 35). A missed exam, except for extreme and dire circumstances, will receive a grade of zero.  In these rare cases, verification and reason for absence is required (Doctor’s note, note from the Dean’s office, etc.). It is your responsibility to provide documentation and contact me prior to the missed class so I can determine if an exam will be allowed to be made up. 

 

Withdrawing from the Course:

The last day to drop the course is Friday, Oct. 16, 2009. Please see your Dean to fill out the appropriate forms.

 

Incompletes:

The policy for receiving an incomplete is outlined in the undergraduate catalog.  An incomplete is issued when, due to an emergency situation, a student prearranges to complete some of the course requirement. 

 

Academic Honesty:

All students are expected to follow the guidelines for academic honesty. (Student handbook 2008-2009 edition, pg 35).  The catalog outlines what constitutes academic dishonesty. In this course, acts of academic dishonesty may include using unauthorized “cheat sheets” on quizzes or exams; copying or obtaining questions and solutions from other students; sharing computer output or solutions, passing off someone else’s work as your own; programming inappropriate formulas/programs into calculators/PDA/cell phones (you can always check with me if you are unsure if a program you have is inappropriate); plagiarizing (copying or cut and pasting) other student’s or previously published work without proper citations; sharing computer output; etc.  If you have questions about whether a particular situation is “dishonest” please ask!!! 

 

Students caught breaking the academic honesty policy of this class will receive a grade of 0 on the assignment and/or an F in the course.  The student will be reported to his/her Dean and the violation will be included in the student’s academic record.

 

Students with Disabilities:

Accommodations for students with documented disabilities will be made according to suggestions from the Office of Academic and Disability Support Services in the Kelley Center.  Please contact Aimee Tiu-Wu, 203-254-4000 x2615, atiu-wu@mail.fairfield.edu.  Please inform me of these arrangements at the beginning of the semester.

 

General Words of Advice:

Feel free to consult with other students or come to office hours if you get stuck. If you find yourself falling behind see me as soon as possible.  Please do not wait until right before exam time.

 

 

For tips on how to have "Success in Math" (as well as your other classes) check out the website:        

http://mathcs.slu.edu/undergrad-math/success-in-mathematics

 

I hope you have a good semester! J

 

DISCLAIMER: The views expressed in this page and all subsequent pages are those of the faculty author and do not necessarily represent those of  Fairfield University or its affiliates.  Materials posted on this website are protected by copyright laws and cannot be copied or replicated without written consent from the author (Laura McSweeney).