Probability for Physicists pp 31-64 | Cite as

# Probability Distributions

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## Abstract

Starting with the examples of distributions in general, the Dirac delta and the Heaviside unit functions are presented, followed by the definition of continuous and discrete random variables and their corresponding probability distributions. Probability functions, probability densities and (cumulative) distribution functions are introduced. Transformations of random variables are discussed, with particular attention given to the cases where the inverse of the mapping is not unique. Two-dimensional cases are treated separately, defining joint and marginal distributions, as well as explaining the variable transformation rules in multiple dimensions.

## References

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*Theory and Problems of Probability and Statistics*, 4th edn. (McGraw-Hill, New York, 2012)Google Scholar - 3.J.J. Brehm, W.J. Mullin,
*Introduction to the Structure of Matter*(Wiley, New York, 1989)Google Scholar - 4.S. Širca, M. Horvat,
*Computational Methods for Physicists*(Springer, Berlin, 2012)zbMATHGoogle Scholar - 5.I. Kuščer, A. Kodre,
*Mathematik in Physik und Technik*(Springer, Berlin, 1993)zbMATHGoogle Scholar

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