Course Information for STOR 435 (Spring 2010)
Introduction to Probability

Class meetings: Tuesday and Thursday 3:30 - 4:45, in Hanes 130

Prerequisites:   A good working knowledge of Mathematics 231-233 (calculus of one and several variables) or equivalent.  Students will need some familiarity with manipulating single and double sums and should be comfortable with standard mathematical notation for sums, products, unions, intersections, sets and so on.  They should be familiar with integration on the line (including the integrals of exponential functions and polynomials) and with multiple integrals in the plane.  We will assume knowledge of some basic facts like the binomial theorem, the geometric series, and the series expansion of the exponential function.

Registration: Enrollment and registration for the course is handled by Charlotte Rogers in the Department Statistics and Operations Research.  Ms. Rogers can be reached at 962.2307, or by email at crogers@email.unc.edu.   The instructor does not have control over the class rolls.  Though the first several lectures are often crowded, there is usually enough space to accomodate students interested in taking the course.
 

Instructor:  Andrew B. Nobel, Department of Statistics and Operations Research

Office: Hanes 308       Phone: 962-1352.

Office Hours:  Monday 2 - 3:15 and Friday 1:30 - 2:30 (new)

 

Grader:  Ms. Sunyoung Shin

Office: Hanes B56    Email: sunyoung@email.unc.edu

Office Hours: Monday 10:30-11:45 and Wednesday 1:30 - 2:45

 

Textbook:   "A First Course in Probabililty",  Edition, by Sheldon Ross.

Calculators: You will need a calculator that can compute exponentials and factorials.  Calculators should be brought to exams.

 
Classroom Protocol: Please show up on time, as late arrivals tend to disturb those already present.  Please refrain from reading newspapers or using laptops during class.   Attendance is not taken in class.  If you are unable to make a lecture, see to it that you obtain the notes from someone else in the class.

 
Homework policy: Homework assignments will be posted on the course web page and will typically be due once a week. Assignments will be collected at the beginning of class on the day they are due. Each homework assignment will be graded: late/missed homeworks will receive a grade of zero.  In computing a student's overall homework score for the course, their two lowest homework scores will be dropped. This latter provision is meant to cover exceptional situations in which a student is unable to turn in an assignment due to circumstances beyond his/her control.  As a general matter, students are expected to turn in every homework assignment.

To receive full credit on the homework assignments, you must clearly label each problem, neatly show all your work (including written justifications of your mathematical arguments), circle or underline your final answers, and staple together the pages of each assignment in the correct order. Please write your name or initials on each page. You should give a clear account of your reasoning in English, and use full sentences where appropriate.

You are allowed to discuss the homework problems with other students, but must prepare each assignment by yourself. Copying of homework is not allowed. Any questions regarding the grading of homeworks should first be addressed to the TA. If you are absent from class when an assignment is returned, you can get your paper from the TA during their office hours.

 
Exams:   There will be two in-class midterm exams, and a comprehensive final examination that will also be in-class. All exams will be closed book and closed notes. Tentative exam dates are as follows.  The final exam will be given at the date and time specified in the official University Final Exam Schedule.

Grading:   The overall course grade will be based on the homework assignments and exams, and will be calculated as follows:

Homework	15%
Midterm 1	22%
Midterm 2	22%
Final	41%

When Midterms 1 and 2 are returned, a rough correspondence between numerical scores and letter grades for that individual exam will be provided.   Any student receiving a grade of D or F should come to the instructor's office hours.  The final course grade is based on a weighted sum of Homework, Midterm and Final scores using the weights above.
 

Syllabus:   We will cover selected material from Chapters 1 - 8 of the text, with particular emphasis on the following topics:

    Probability models for random experiments

    Conditional probabilities and independence

    Discrete and continuous random variables

    Important discrete and continuous distributions

    Jointly distributed random variables

    Definition and basic properties of expectations

    Laws of large numbers and the central limit theorem

    Basic inequalities for probabilities and expectations

    Conditional Expectations (as time permits)


Other Texts: You should feel free to consult other textbooks regarding the material in the course, including a good calculus textbook.  Other probability books that may be useful are:

   ``Probability'' by Jim Pitman, published by Springer

   ``Introduction to Probability'' by Douglas G. Kelly, published by Macmillan

   ``Probability and Random Processes'' by G.R. Grimmett and D.R. Stirzaker, published by Oxford
 

Honor Code: Students are expected to adhere to the UNC honor code at all times. Violations of the honor code will be prosecuted.


Study tips:     

1. Keep up with the reading and homework assignments.

2. Look over the notes from the lecture k before attending lecture k+1.   This will help keep you on top of the course material.  Ideas from one lecture often carry over to the next: you will get much more out of the material if you can maintain a sense of continuity and ``big picture''.

3. Read the book carefully *before* doing the homework.  Trying to find the right section, formula, or paragraph for a particular problem often takes as much time, and tends to create more confusion than it resolves.  Each chapte of the book contains many examples illustrating the ideas presented there.  Some of the examples are rather long, and require more effort to read and understand.  When you first read the chapter, don't feel as if you need to read through every example: focus first on the shorter, simpler examples, and then look at the longer, more complicated examples afterwards.

4. Keep careful track of any concepts and ideas that you are unclear about, and make efforts to master these in a timely fashion, using the class notes, the text, office hours, and outside reading if necessary.

5. One good way of seeing if you understand an idea or concept is to write down the associated definitions and basic facts, without the aid of the book or your notes, in full, grammatical sentences.  Translating ideas from mathematics to complete English sentences, and back again, is an important component of the course.

6. Homework plays two important roles in the course.  First, it provides an opportunity to actively think about, engage with, and learn the course material.   In addition, homework provides feedback on your understanding of the material.  Carefully look over your corrected homework assignments.  Most students do relatively well on the homework: even if you received a good score, make sure to note and understand or correct any mistakes you made on the problems.

7. Begin studying for exams one week before they are given.  Look over your notes, homework, and the text.  Write up a study guide containing the main concepts and definitions being covered, and use this to get a clear picture of the overall landscape of the material.