Abstract
The main properties of discrete probability distributions are presented. Joint, marginal, and conditional distributions are introduced, with the main statistical indicators: average, variance, etc. The problem of determining the probability distribution under variable transformation is presented. The most frequently used discrete distribution are introduced: Bernoulli, binomial, multinomial and Poisson, and their properties are discussed. The law of large numbers is introduced, and its importance under the frequentist approach to probability is discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The coefficients present in the binomial distribution are the same that appear in the expansion a binomial raised to the nth power, (a + b)n. A simple iterative way to compute those coefficients is known as Pascal’s triangle . In different countries this triangle is named after different authors, e.g., the Tartaglia’s triangle in Italy, Yang Hui’s triangle in China, and so on. In particular, the following publications of the triangle are present in literature: • India: published in the tenth century, referring to the work of Pingala, dating back to fifth–second century bc. • Persia: Al-Karaju (953–1029) and Omar Jayyám (1048–1131) • China: Yang Hui (1238–1298), see Fig. 2.3 • Germany: Petrus Apianus (1495–1552) • Italy: Nicolò Fontana Tartaglia (1545) • France: Blaise Pascal (1655)
Yang Hui (杨辉 ) triangle as published by Zhu Shijie (朱世杰 ) in Siyuan yujian, (四元玉鉴 ) Jade Mirror of the four unknowns (1303), public domain image.
D. Zwillinger, S. Kokoska, CRC Standard Probability and Statistics Tables and Formulae (Chapman & Hall, New York, 2000)
D.N. Joanes, C.A. Gill, Comparing measures of sample skewness and kurtosis. J. R. Stat. Soc. D 47(1), 183–189 (1998). https://doi.org/10.1111/1467-9884.00122
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Lista, L. (2023). Discrete Probability Distributions. In: Statistical Methods for Data Analysis. Lecture Notes in Physics, vol 1010. Springer, Cham. https://doi.org/10.1007/978-3-031-19934-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-19934-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-19933-2
Online ISBN: 978-3-031-19934-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)