MATH371 - Introduction to Probability & Statistics
William Abrams
Ruffner 337
395-2188
Office Hours: MWF 10 - 11:20, TR 10:45 - 11:20, or by appt.
Course Description: Introduction to Probability and Statistics. Theory of probability; expected
values of random variables; discrete and continuous probability distributions. Prerequisite:
MATH 270 and 361. 3 credits. Offered every spring.
Course Objective:
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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.
Text: Hogg and Tannis, Probability and Statistical Inference, 8th ed. Pearson. 9780321584755.
You will also need a scientific calculator, the equivalent of the TI-83 or 84. If you want to use
something else you should talk to me first.
Grading: You will have regular homework, two tests, and a comprehensive Final Exam. The
tests will be worth 20% each, the final will be worth 20%, and the homework will be worth 35%.
The last 5% of your grade is for Culture Points. Standard grading rates apply: 90 - 100 is an A,
80 - 89 is a B, 70 - 79 is a C, 60 - 69 is a D, and anything below a 60 is failing.
Dates
TENTATIVE SECTIONS COVERED
1/19 - 1/21
Basic Probability 1.1 - 1.3
1/24-1/28
Enumeration and Conditional Probability 1.3 - 1.4
1/31-2/4
Independent Events and Baye's Theorem 1.4 - 1.5
2/7-2/11
Discrete Random Variables, Expectation, Mean, 2.1 - 2.3
2/11-2/15
Variance, Standard Deviation, Bernoulli Trials, Binomial Distribution,
2/14-2/18
Moment Generating Function, Poisson Distribution, 2.5,2.6, Test I
2/21-2/25
Continuous Data and Data Analysis, 3.1, 3.2
2/28-3/4
Random Variables, 3.3
3/7-3/11
SPRING BREAK
3/14-3/18
Various Distributions, 3.4 - 3.6
3/21 - 3/25
Various Distributions, Test II
3/28-4/1
Two Random Variables and Correlation, 4.1,4,2
4/4-4/8
Functions of Random Variables, 5.1,5.2
4/11-4/15
More Random Variables and Moment Generating Function Techniques, 5.3,5.4
4/18-4/22
Random Variables and Normal Distributions, 5.5, Test III
4/25-4/29
Central Limit Theorem, 5.6
5/6
FINAL EXAM, 11:30 - 2
Honor Code: Every assignment you turn in for this class is covered by the Longwood College
Honor Code. Please be sure that you know whether you are allowed to collaborate and which
resources you are allowed to use before you start an assignment. For quizzes, tests, and the
homework, you may not consult with any other person. For the quizzes and homework you may
use your book and notes. The tests will be closed book. You may always consult with the
instructor.
Homework: There will be several different kinds of homework. Doing problems is the best way
to learn this material, so homework is very important. Traditional homework will be assigned
and collected most Fridays. It is to be your own work. I might also suggest problems in the
homework that are worth doing, even though they will not be collected. These you can work on
using any resources you want. In addition we will do board work, hopefully at least three times
during the semester. In board work, you will be given a variety of homework problems to
prepare. If your name is randomly selected for a problem, you are to go up to the board and
present your solution to the problem. Board work will be graded on presentation as well as
correctness. I do not intend to be particularly strict enforcing the honor code when we do board
work. However, I will expect you to understand the solution you are presenting.
Culture Club Points: Culture Points are awarded for doing a write up of an out-of-class event
that you attended involving mathematics. In particular, submitting a problem of the month (and
letting me have a copy of your solution) or attending a mathematical colloquium and doing a
short write up will count as one culture point. Attending two math club meetings and doing a
short write up of each will count as one culture point. Consult with me if you have other ideas.
Attendance: You are expected to attend every class. It has been my experience that those
students who do not attend class fail. You don't want to fail, so please attend class.