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 Readings
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.
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