Statistics Primer

Instructor: Andras Vetier

For a great majority of students learning any abstract theory is to see the down to earth meaning of notions and methods. These for probability and statistics can be experienced only by making a large number of experiments repeated many times. Performing experimtnts in a large number and then drawing (correct) conclusions is a complicated task. This is exactly what we will do along the course.

The goals of the course are:

• to learn the most important notions and methods of probability theory and statistics
• to get an experience of the real life meaning of these notions and methods

The learning outcomes of the course:

• students will learn the basic notions and results of probability theory and statistics.
• they will learn not only theoretical notions but - through simulations - they will have a "real life experience" of the meaning of the notions and methods.

Lecture 1.

Basic notions: Random numbers, Basic properties of probability

Lecture 2.

Conditional probability, Independence of events

Lecture 3.

Discrete random variables and distributions

Lecture 4.

Expected value of discrete distributions

Lecture 5.

Continuous distributions

Lecture 6.

Expected value of continuous distributions, Standard deviation

Lecture 7.

Normal distributions

Lecture 8.

Two-dimensional distributions

Lecture 9.

Regression

Lecture 10.

Confidence intervals

Lecture 11.

Hypothesis Tests

Lecture 12.

Final exam

Assessment and grading:

Attendance is mandatory. Homework will be assigned regularly. The final test will be based to a significant extent on homework assignments. There will be a final exam (worth 70%). The homeworks are worth 30%.

Literature:

• Sheldon Ross: A First Course in Probability, Prentice Hall, 2006 ISBN 0-13-185662-6
• Jim Pitman: Probability, Springer, 1993, ISBN 0-387-97974-3
• Ian F. Blake: An Introduction to Applied Probability, Wiley
• Paul L. Meyer: Introductory Probability and Statistical Applications, Addison-Wesley Publishing Company
• Gary Smith: Statistical Reasoning, Allyn And Bacon, Inc ISBN 0-205-08295-5
• Roy D. Yates - David J. Goodman Probability and Stochastic Processes Wiley 2005 ISBN 0-471-27214-0