Random Variables and Probability Distributions

  • Thomas Cleff


In the previous chapter, we learned about various principles and calculation techniques dealing with probability. Building on these lessons, we will now examine some theoretical probability distributions that allow us to make inferences about populations from sample data. These probability distributions are based on the idea of random variables. A random variable is a variable whose numerical values represent the outcomes of random experiments. Random variables are symbolized with capital letters such as “X”. The individual values of random variables are represented either with a capital Roman letter followed by a subscript “i” (e.g. “Xi”) or with the lower case of the random variable letter (e.g. “x”). Generally, there are two types of random variables:


  1. Bortz, J., Schuster, C. (2010). Statistik für Sozialwissenschaftler, 7th Edition. Berlin, Heidelberg: Springer.Google Scholar
  2. de Moivre, A. (1738). Doctrine of Chance, 2nd Edition. London: Woodfall.Google Scholar
  3. von Mises, R. (1957). Probability, statistics and truth, 2nd revised English Edition. New York: Dover Publications.Google Scholar
  4. Swoboda, H. (1971). Exakte Geheimnisse: Knaurs Buch der modernen Statistik. Munich, Zurich: Knaur.Google Scholar

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Authors and Affiliations

  • Thomas Cleff
    • 1
  1. 1.Pforzheim Business SchoolPforzheim University of Applied SciencesPforzheimGermany

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