Probability theory originated in the consideration of gambling problems, but has become an important tool for scientists, engineers, medical practitioners, lawyers, and people working in business. A wide variety of phenomena are characterized by randomness and uncertainty, which is measured by probability. Probability models also play a fundamental role in the statistical analysis of data.
The aim of the course is to provide an introduction to the concepts of probability. The course will cover the basic ideas used to describe aspects of randomness, such as events, random variables, independence, and conditional probability, with emphasis on the methods, calculation, and applications of probability. The topics treated are: combinatorics; probability models; rules of probability; conditional probability; independence; random variables; expectation and standard deviation; games of chance; common discrete distributions --- uniform, binomial, hypergeometric, geometric, negative binomial, and Poisson --- and their interrelationships; univariate and multivariate density and distribution functions; change of variable formulas for densities; common continuous distributions --- beta, Cauchy, chisquare, exponential, gamma, lognormal, normal, uniform --- and their interrelationships; moment generating functions; laws of large numbers and the central limit theorem.
Prerequisites: Math 20000 or 20500 (or equivalent), or permission from the instructor. Completion of one of the Common Core sequences in the Biological or Physical Sciences is highly recommended. No prior exposure to probability theory is required or assumed.
The course assistants also will have office hours (beginning in the second week).
One nice feature of this text is that each chapter has a set of self-test problems, with answers in Appendix B. Although these problems will not be assigned as homework, you should try working as many of them as you can, to develop your skills.
The eighth edition was used in this course last year; the seventh edition was used the previous three years. The 7th and 8th editions are similar in content. In the preface to the 8th edition, Ross says that there are many new exercises and examples, some new sections, and some new text material; see page xii for details. Consequently the pagination and enumeration of items is different between the two editions. It is best if you have the 8th edition, but you can get by with the 7th. Reading and homework assignments will specify the pages/problems for both editions, in cases where they differ.
Other References:
Pitman, Jim (1993), Probability, (First edition)
Springer-Verlag.
Feller, William (1968), An Introduction to Probability Theory
and Its Applications, Volume I Third Edition. Wiley.
Pitman is pitched at somewhat lower level than Ross. It is very readable and has some useful summaries.
Feller's book is a classic. It only covers discrete probability, but goes very deep.
Are you getting a degree this quarter? If so, please notify the instructor by email at the beginning of the term.
Good will points: While not a formal component to your grade, you can earn good will points by speaking up in class -- tell me what goes in those blanks in the lecture template -- and/or coming to office hours. Good will points are good to have if you ever ask me to write a recommendation for you. They are also good to have if your course grade is on the borderline between two possibilities; good will points can nudge you into the higher category.
There will be weekly homework assignments. Homework is due in class on the due date. Your solutions must be written legibly and intelligibly in clear English. Use complete sentences, and organize your thoughts for maximum readability by the graders. Papers that don't meet these standards may be rejected and scored as 0. Include your name, date, and homework number on the first page of your assignment. Staple the pages together.
You may discuss homework problems with other students (it is encouraged!) but you must write them up independently. If you have collaborated in any fashion, you must explain fully the nature of that collaboration in writing and cite the name of every collaborator. Show your work; how you arrive at your answer more important than the final numerical result (which in many cases you can look up in Appendix A of Ross). Duplication of homework solutions prepared in whole or in part by someone else is not permitted.
Solutions will be posted in the display cases outside Eckhart 133 shortly after the due date and will be put on reserve in Eckhart Library. The display case for Stat251 is diagonally opposite the water coolers. Make a habit of consulting the solutions and comparing them with your own, since there's only so much feedback you can get from the grader. Even if you got the correct answer, you may learn something from the TA's model solutions. The TA's will be available during their office hours to discuss questions you may have about the homework.
THE OFFICIAL COURSE POLICY IS: NO LATE HOMEWORK WILL BE ACCEPTED. In cases with documented extenuating circumstances, the instructor (not the TA's) may agree to accept late homework that is turned in before the answers are posted in the display case. Otherwise, late assignments will receive a score of zero. As mentioned previously, your lowest homework score will be dropped. You thus have the option of skipping one homework, whatever may be the reason. We encourage you, though, to try to not make use of that option. The homework is intended to help you master the material so that you can do well on the exams. Also, if you skip a homework early on, then a low homework score later on will hurt you.
Some homework sets may have extra-credit problems. All the points you earn from these problems will count towards your final grade.
In return for your timely submission of homework, we will make every effort
to return graded homework promptly. This rapid feedback
should help you be aware of any problems in your own understanding of the
material.