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2024 | OriginalPaper | Chapter

16. Probability: From Sample Spaces to Conditioning

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Key Topics in This Chapter: Mainly Quantitative

In this chapter, we present the basic concepts of probability theory which are indispensable for quantitative risk management. A straightforward approach is chosen, avoiding more advanced concepts like measure theory. Primarily we consider the following:
  • Randomness, experiments, sample spaces, random events, and their role in risk modelling.
  • Sets and their algebra.
  • The concept of probability, including the Kolmogorov axioms.
  • The concept of random variables.
  • Discrete and continuous random variables and their probability mass function, probability density function, and cumulative distribution function.
  • Characteristics of random variables (expectation, variance, covariance, correlation, skewness, kurtosis).
  • Marginal distribution functions.
  • The concept of conditional probability, conditioning, and the laws of total expectation and variance.

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Metadata
Title
Probability: From Sample Spaces to Conditioning
Author
Herfried Kohl
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-71272-2_16

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