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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
J.C. Ferreira, Introduction to the theory of distributions, Pitman Monographs and Surveys in Pure and Applied Mathematics (Addison Wesley Longman Ltd., Harlow, 1997)
M.R. Spiegel, J. Schiller, R.A. Srinivasan, Theory and Problems of Probability and Statistics, 4th edn. (McGraw-Hill, New York, 2012)
J.J. Brehm, W.J. Mullin, Introduction to the Structure of Matter (Wiley, New York, 1989)
S. Širca, M. Horvat, Computational Methods for Physicists (Springer, Berlin, 2012)
I. Kuščer, A. Kodre, Mathematik in Physik und Technik (Springer, Berlin, 1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Širca, S. (2016). Probability Distributions. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-31611-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-31609-3
Online ISBN: 978-3-319-31611-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)