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2024 | OriginalPaper | Chapter

17. Probability: Auxiliary Concepts, Tools, and Results

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Key Topics in This Chapter: Mainly Quantitative

In this chapter, we present several helpful and indispensable tools for dealing with random variables and their distributions. Especially, we discuss the following:
  • Generating functions.
  • The concept of entropy and the maximum entropy principle (MEP).
  • Inequalities for random variables (Markov, Chebyshev, Cantelli, Jensen, Cauchy-Schwartz) and some of their applications.
  • Limit theorems (central limit theorem, and others).
  • Some results from combinatorics are needed for counting things.

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Literature
go back to reference Fick E, Sauermann G (1990) The quantum statistics of dynamic processes. SpringerCrossRef Fick E, Sauermann G (1990) The quantum statistics of dynamic processes. SpringerCrossRef
go back to reference Gradshteyn IS, Ryzhik IM (1965) Tables of integrals, series, and products. Academic Press Gradshteyn IS, Ryzhik IM (1965) Tables of integrals, series, and products. Academic Press
go back to reference Kapur JN (1989) Maximum-entropy models in science and engineering. Wiley Kapur JN (1989) Maximum-entropy models in science and engineering. Wiley
go back to reference Ross SM (2010) Introduction to probability models. Academic Press Ross SM (2010) Introduction to probability models. Academic Press
go back to reference Widder DV (1989) Advanced calculus. Dover Publications Widder DV (1989) Advanced calculus. Dover Publications
Metadata
Title
Probability: Auxiliary Concepts, Tools, and Results
Author
Herfried Kohl
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-71272-2_17

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