MATH371 - Introduction to Probability & Statistics

Class Syllabus - Spring 2010

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Course Description:   This course is a mathematical introduction to probability theory and statistics.   Topics will include probability, mathematical expectation, discrete & continuous probability distributions, multivariate distributions, and sampling distribution theory.  An emphasis will be placed on the application of these concepts.   In order to increase the likelihood of success in this course it is recommended that the student attend class without fail, religiously work the homework, read the textbook, focus on understanding the concepts (not just the rote computations), and seek help from the professor and other sources (library, web, tutoring, etc.) when needed. 

Course Objectives:   Students completing this course should be able to:

  • understand the concepts of sample space, event, and random variable.
  • use methods of enumeration, conditional probability, independent events, and Bayes's Theorem to solve basic probability problems.
  • understand and apply standard probability models including the Bernoulli, Binomial, Poisson, Uniform, Exponential, Gamma, Chi-Square and Normal distributions.
  • understand and apply the concepts of mean, variance and standard deviation.
  • understand and apply the concept of mathematical expectation.
  • perform basic probability computations using multivariate distributions. 
  • understand and apply the concept of a sampling distribution.
  • understand and apply the central limit theorem and the law of large numbers.

Prerequisites:  Differential and integral calculus including infinite series (MATH261 and MATH262 at Longwood).  It is also preferred (but not required) that the student has had some exposure to multivariate calculus (MATH361 at Longwood), to logic and proof (MATH300 or CMSC206 at Longwood), and to introductory level statistics (MATH171 or MATH270 at Longwood or AP Statistics in high school).  If you are not sure you meet the prerequisites for this course, especially if you have none of the preferred (but not required) prerequisites, then please see me as soon as possible.

Professor:  Dr. M. Leigh Lunsford.  For Dr. Lunsford's office location, phone number, email address, schedule (including office hours), and other general information, go to her homepage:  http://www.mathspace.com/Lunsford/

Meeting Time & Location:  TR 11:00-12:15 pm, Ruffner 356

Textbook:    Schaum's Outline of Probability and Statistics, 3rd Edition, M. R. Spiegel, J. Schiller, R.A. Srinivasan, ISBN 978-0-07-154425-2, McGraw-Hill Companies, 2009.

Required Technology/Computer Configurations: 

  • The TI-83 or the TI-83 Plus calculator is required.  If you do not use the TI-83 then you will be responsible for knowing how to use your particular calculator.   You will not be allowed to use a calculator that does symbolic mathematics.

  • Microsoft Excel configured with the Data Analysis Add-In

  • We will occasionally use Maple to view some animations, etc.

  • Also we may use the website Virtual Laboratories in Probability and Statistics.  To run the applets on this website you will need to make sure your machine is configured with MathML and the appropriate Java runtime environment.  Directions on how to configure your machine are contained on the Virtual Labs website.  A former professor of mine, Dr. Kyle Siegrist, at the University of Alabama in Huntsville, has created this great site!

Determination of Course Grade:

31% - Midterm Exam

31% - Quizzes and/or Hand-In Homework

7% - Mathematics Cultural Points (cults)
31% - Comprehensive Final

Grades will be assigned on a ten point scale (90's A; 80's B; 70's C; 60's D; 50's and below F).

Honor System:  I expect you to conform to the Longwood University Honor System as contained in the Student Handbook.  All material handed in to me (homework, quizzes, tests) must be pledged.

Homework:  Your homework assignments will be given on the Assignments page of this website.  You will have two types of homework assignments.  I will assign practice homework and occasionally homework to hand in. 

Practice Homework:  Just like with anything else worthwhile in life, one must practice to become proficient at mathematics.  I will post your practice problems on the Class Pace/Assignments page.  You should endeavor to work practice problems before the next class period.  You should not have more than 1 or 2 problems which you cannot work.  If you cannot work all but 1 or 2 of your homework problems then you need to see me for help before the next class period!  I encourage you to work together on your practice homework.   I will be selecting problems for your quiz problems that are very similar to the practice homework.

Hand-In Homework:  Hand-in problems will be due on the date specified on this website (see the Assignments page).  Hand-in homework will generally be either theoretical in nature or involve the use of technology.   Late hand-in homework will not be accepted, period.  Please see the make-up policy below for additional information.

Quizzes:   Approximately every week a short quiz will be given.  These quizzes will be administered outside of class by me (during my office hours) or by the departmental secretary during select times.  I will try to give a notice of at least two days for quiz due dates but typically the quiz for each week will be available after class on Tuesday and due before class on Thursday.  These quizzes will be based on your practice homework assignments and our class discussions.  Once the due date for a quiz has expired there will be no make-ups for that quiz, period.  All quizzes must be pledged.  Please see the make-up policy below for additional information.  Information about quizzes, the topics they cover, and their dates will be given on the Assignments page.

Mathematics Cultural Points (cults):  In order to receive the full 7% credit for mathematics cultural points you must earn at least 10 cults.  To determine how to earn cults please click here.  Please note the deadline requirements for submitting cults.

Midterm Exam:  A minimum of a one week notice will be given for the midterm exam date.  A make-up exam must be scheduled before the exam date.  If the exam has already been given and you have not previously scheduled a make-up, then you will receive a zero on that exam.  Please see the make-up policy below for additional information. 

Sample Tests and Quizzes  On my website I have provided copies of quizzes and tests I have previously given in classes similar to this class.  Please note that your tests and quizzes will not be exactly the same as these tests and quizzes.  

Final Exam:  The final exam for this course will be comprehensive.  You cannot miss the final - failure to take the final exam will automatically result in an F grade for the course.

Final Exam Date:   Wednesday, April 28, 3:00 - 5:30 p.m.

Extra Credit:  Extra Credit will NOT be given - period.

Attendance & Excused Absences:   Students are expected to attend all classes.  As an upper level college student you already know that attendance, especially non-attendance, has a direct impact on class performance.  The following college attendance policy will be followed per the Class Attendance section of the Academic Regulations chapter of the Longwood University Undergraduate Catalog:  Missing 10% of class meetings may result in a lowering of one letter grade.   Missing 25% of class meetings for any reason will result in an automatic “F” for the course.  Absences are excused only for illness, college sponsored activities, and recognizable emergencies.  You must have the proper documentation for an excused absence.  Student Health Services can provide documentation only for students hospitalized locally or absent at the direction of Student Health Services personnel You must also assume full responsibility for all material covered during your absence, including scheduling any make-up quizzes or exams.  A grade of "0" will be assigned for all work missed due to unexcused absences.

Make-up Policy:    Make-up assignments will be given only when the reason for missing the assignment meets the criteria for an excused absence (see above).  Except in the case of emergencies, make-up assignments must be turned in before the due date of the assignment being made-up (i.e. you should plan ahead if you know you are going to miss class).  As a general rule, you can expect that make-up tests and quizzes will more difficult than regularly scheduled tests.  If you have a recognizable emergency, please contact me as soon as you can to discuss your make-up options.

Resources for Students Learning Probability & Statistics:   I want you to consider me to be your number one resource!  In addition to seeing me during my office hours, you are welcome to call me or send me email if you have questions about your homework.  If you are unable to see me during my office hours please make an appointment with me! 

Class Schedule:  Below is a tentative class schedule.  For a more detailed schedule, including homework assignments, please see the Assignments page.

Week of Class Topics Covered

1

Basic Concepts of Probability

Properties of Probability

Methods of Enumeration

2

More on Methods of Enumeration

Conditional Probability

Independent Events

3

Bayes' Theorem

Discrete and Continuous Random Variables

4

More on Discrete and Continuous Random Variables

Mathematical Expectation

The Mean, Variance, and Standard Deviation

5

Bernoulli Trials and the Binomial Distribution

The Moment-Generating Function

6

The Poisson Distribution

The Uniform and Exponential Distributions

7

The Gamma and Chi-Square Distributions

MidTerm Exam

8

Distributions of Functions of a Random Variable

Distributions of Two Random Variables

9

The Correlation Coefficient

Conditional Distributions

10

Transformations of Random Variables

Several Independent Random Variables

11

Distributions of Sums of Random Variables

The Normal Distribution

12

Random Functions Associated with the Normal Distributions

The Central Limit Theorem

13

Approximations for Discrete Distributions

The Bivariate Normal Distribution

14

Point Estimation

Confidence Intervals for Means

15

Comprehensive Final Exam

 

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