Feller, William Formerly, Department of Mathematics, Princeton University, Princeton, New Jersey.
- Sample space
- Probabilities in finite spaces
- Probabilities in infinite spaces
- Conditional probability—independence
- Independent trials
- Dependent trials; Markov chains
- Random variables and their distributions
- Laws of large numbers
- Additional Reading
The chance likelihood of a specified event or circumstance, usually expressed as the ratio of the number of times that event occurs to the large number of trials that take place to observe its occurrence or failure to occur. Although probability theory derives its notion and terminology from intuition, a vague statement such as “John will probably come” is as remote from it as the statement “John is forceful and energetic” is remote from mechanics. Probability theory constructs abstract models, mostly of a qualitative nature, and only experience can show whether these reasonably describe laws of nature or life. As always in mathematics, only logical relations and implications enter the theory, and the notion of probability is just as undefinable (and as intuitive) as are the notions of point, line, or mass. An actual assignment of numerical probabilities is frequently unnecessary or impossible. For example, telephone exchanges are based on a theoretical comparison of several possible systems; only the optimal ones are built and the others discarded. Thus a huge industry depends on theoretical models of exchanges which will never exist.
The content above is only an excerpt.
for your institution. Subscribe
To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.
to your librarian. Recommend
Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.
AccessScience provides the most accurate and trustworthy scientific information available.
Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Contributors include more than 9000 highly qualified scientists and 43 Nobel Prize winners.
MORE THAN 8700 articles covering all major scientific disciplines and encompassing the McGraw-Hill Encyclopedia of Science & Technology and McGraw-Hill Yearbook of Science & Technology
115,000-PLUS definitions from the McGraw-Hill Dictionary of Scientific and Technical Terms
3000 biographies of notable scientific figures
MORE THAN 19,000 downloadable images and animations illustrating key topics
ENGAGING VIDEOS highlighting the life and work of award-winning scientists
SUGGESTIONS FOR FURTHER STUDY and additional readings to guide students to deeper understanding and research
LINKS TO CITABLE LITERATURE help students expand their knowledge using primary sources of information