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Discrete Random Variables and Probability Distributions

  • Jay L. Devore
  • Kenneth N. Berk
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

Whether an experiment yields qualitative or quantitative outcomes, methods of statistical analysis require that we focus on certain numerical aspects of the data (such as a sample proportion x/n, mean \( \bar{x} \), or standard deviation s). The concept of a random variable allows us to pass from the experimental outcomes themselves to a numerical function of the outcomes. There are two fundamentally different types of random variables—discrete random variables and continuous random variables. In this chapter, we examine the basic properties and discuss the most important examples of discrete variables. Chapter 4 focuses on continuous random variables.

Bibliography

  1. Durrett, Richard, Elementary Probability for Applications, Cambridge Univ. Press, London, England, 2009.CrossRefGoogle Scholar
  2. Johnson, Norman, Samuel Kotz, and Adrienne Kemp, Univariate Discrete Distributions (3rd ed.), Wiley-Interscience, New York, 2005. An encyclopedia of information on discrete distributions.CrossRefGoogle Scholar
  3. Olkin, Ingram, Cyrus Derman, and Leon Gleser, Probability Models and Applications (2nd ed.), Macmillan, New York, 1994. Contains an in-depth discussion of both general properties of discrete and continuous distributions and results for specific distributions.Google Scholar
  4. Pitman, Jim, Probability, Springer-Verlag, New York, 1993.CrossRefGoogle Scholar
  5. Ross, Sheldon, Introduction to Probability Models (9th ed.), Academic Press, New York, 2006. A good source of material on the Poisson process and generalizations and a nice introduction to other topics in applied probability.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Statistics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsIllinois State UniversityNormalUSA

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