Abstract
The term probability refers to the study of randomness and uncertainty. In any situation in which one of a number of possible outcomes may occur, the theory of probability provides methods for quantifying the chances, or likelihoods, associated with the various outcomes. The language of probability is constantly used in an informal manner in both written and spoken contexts. Examples include such statements as “It is likely that the Dow Jones Industrial Average will increase by the end of the year,” “There is a 50–50 chance that the incumbent will seek reelection,” “There will probably be at least one section of that course offered next year,” “The odds favor a quick settlement of the strike,” and “It is expected that at least 20,000 concert tickets will be sold.” In this chapter, we introduce some elementary probability concepts, indicate how probabilities can be interpreted, and show how the rules of probability can be applied to compute the probabilities of many interesting events. The methodology of probability will then permit us to express in precise language such informal statements as those given above.
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- 1.
Iff is an abbreviation for “if and only if.”
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However, the multiplication property is satisfied if P(B) = 0, yet P(A|B) is not defined in this case. To make the multiplication property completely equivalent to the definition of independence, we should append to that definition that A and B are also independent if either P(A) = 0 or P(B) = 0.
Bibliography
Durrett, Richard, Elementary Probability for Applications, Cambridge Univ. Press, London, England, 2009. A concise presentation at a slightly higher level than this text.
Mosteller, Frederick, Robert Rourke, and George Thomas, Probability with Statistical Applications (2nd ed.), Addison-Wesley, Reading, MA, 1970. A very good precalculus introduction to probability, with many entertaining examples; especially good on counting rules and their application.
Olkin, Ingram, Cyrus Derman, and Leon Gleser, Probability Models and Application (2nd ed.), Macmillan, New York, 1994. A comprehensive introduction to probability, written at a slightly higher mathematical level than this text but containing many good examples.
Ross, Sheldon, A First Course in Probability (8th ed.), Prentice Hall, Upper Saddle River, NJ, 2010. Rather tightly written and more mathematically sophisticated than this text but contains a wealth of interesting examples and exercises.
Winkler, Robert, Introduction to Bayesian Inference and Decision (2nd ed.), Probabilistic Publishing, Sugar Land, Texas, 2003. A very good introduction to subjective probability.
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© 2012 Springer Science+Business Media, LLC
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Devore, J.L., Berk, K.N. (2012). Probability. In: Modern Mathematical Statistics with Applications. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0391-3_2
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DOI: https://doi.org/10.1007/978-1-4614-0391-3_2
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