Abstract
What do we mean by saying that an event occurs randomly with a certain probability? Answering this simple question is the objective of this chapter and our answer forms the foundation for all of the material presented in the text. The existence of randomness is often taken for granted, much like the existence of straight lines in geometry, and the assignment of probabilities to events is often assumed axiomatically. The pervasive use of the word “probability” seems to imply that randomness is the rule rather than the exception. One hears of probabilities being ascribed to such diverse things as the weather, the electability of a presidential candidate, the genetic makeup of a child, the outcome of a sporting event, the chance of winning at blackjack, the behavior of elementary particles, the future marriage prospects of two friends, quantum physics, and the wonderfully incessant gyrations of the stock market.
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Bibliographic Notes
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K.L. Chung. Elementary Probability Theory with Stochastic Processes. Springer-Verlag, 1979.
A.B. Clarke and R.L. Disney. Probability and Random Processes: A First Course with Applications. John Wiley and Sons, 1985.
W. Feller. An Introduction to Probability Theory and Its Applications-Volume I. John Wiley and Sons, 1968.
W. Feller. An Introduction to Probability Theory and Its Applications-Volume II. John Wiley and Sons, 1968.
B.V. Gnedenko. The Theory of Probability, second edition. Chelsea, 1963.
R.W. Hamming. The Art of Probability-for Scientists and Engineers. Addison-Wesley, 1991.
P.G. Hoel, S.C. Port, and C.J. Stone. Introduction to Probability Theory. Houghton Mifflin, 1971.
A. Kolmogorov. Foundations of the Theory of Probability. Chelsea, 1950. A. Rényi. Foundations of Probability. Holden-Day, 1970.
S.M. Ross. An Introduction to Probability Models. Academic Press, 1972.
R. von Mises. Mathematical Theory of Probability and Statistics. Academic Press, 1964.
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Nelson, R. (1995). Randomness and Probability. In: Probability, Stochastic Processes, and Queueing Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2426-4_2
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DOI: https://doi.org/10.1007/978-1-4757-2426-4_2
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