Integer-Valued and Discrete Random Variables

  • Anirban DasGuptaEmail author
Part of the Springer Texts in Statistics book series (STS)


In this chapter, we introduce the concept of random variables and their distributions. In some sense, the entire subject of probability and statistics is about distributions of random variables. Random variables, as the very name suggests, are quantities that vary over time or from individual to individual, and the reason for the variability is some underlying random process. We try to understand the behavior of a random variable by analyzing the probability structure of that underlying random mechanismor process. Random variables, like probabilities, originated in gambling. Therefore, the random variables that come to us more naturally are integer-valued random variables; e.g., the sum of the two rolls when a die is rolled twice. Integervalued random variables are special cases of what are known as discrete random variables. We study integer-valued and discrete random variables and their basic properties in this chapter. Random variables with an intrinsically more abstract and complex structure will be studied after we introduce probability density functions.


Cumulative Distribution Function Independent Random Variable Sample Space Discrete Random Variable Continuous Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alon, N. and Spencer, J. (2000). The Probabilistic Method, Wiley, New York.zbMATHCrossRefGoogle Scholar
  2. Chow, Y. and Studden, W. (1969). Monotonicity of the variance under truncation and variations of Jensen’s inequality, Ann. Math. Statist., 40, 1106–1108.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Erdös, P. and Rényi, A. (1970). On a new law of large numbers, J. Anal. Math., 23, 103–111.zbMATHCrossRefGoogle Scholar
  4. Erdös, P. and Révész, P. (1975). On the length of the longest head-run, Colloq. Janos Bolyai Math. Soc., Topics Inform. Theory I., 16, 219–228.Google Scholar
  5. Paley, R.E. and Zygmund, A. (1932). A note on analytic functions in the unit circle, Proc. Cambridge Philos. Soc., 28, 266–272.CrossRefGoogle Scholar
  6. Rao, C.R. (1973). Linear Statistical Inference and Applications, Wiley, New York.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Dept. Statistics & MathematicsPurdue UniversityWest LafayetteUSA

Personalised recommendations