Handbook of probability
type: Item
instance of: scholarly article
zbMATH Open document ID: 1302.60001
DOI: 10.1002/9781118593103
author: Ionut Florescu
author: Ciprian A. Tudor
publication date: 2014-01-08T00:00:00Z
Mathematics Subject Classification ID: 60-00
zbMATH DE Number: 6243671
zbMATH Keywords: probability theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1002/9781118593103
OpenAlex ID: W643478325
title: Handbook of probability
review text: The present book provides the fundamental notions of probability theory, which are summarized in 14 chapters.NEWLINENEWLINEChapters 1 and 2 deal with the basic definitions of probability theory, such as probability spaces, sigma algebras, and probability measures. The basic properties of probability measures are presented and the definition of conditional probability is given.NEWLINENEWLINEChapters 3, 4, and 5 present a detailed study of random variables. After a general discussion of random variables in Chapter~3, discrete and continuous random variables are analysed in Chapters 4 and 5, respectively. The most popular discrete distributions, such as discrete uniform distribution, Bernoulli distribution, binomial distribution, geometric distribution, negative binomial distribution, hypergeometric distribution and Poisson distribution, are introduced and their properties are discussed in Chapter~4, while Chapter~5 presents the most commonly used families of the continuous distributions, such as uniform distribution, exponential distribution, normal distribution, gamma distribution, beta distribution, Student \(t\)-distribution, Pareto distribution, log-normal distribution, Laplace distribution, double exponential distribution.NEWLINENEWLINEIn Chapter 6, methods of generating random variables are discussed. This is done for both univariate and multivariate random variables. Chapter~7 deals with random vectors, where both the discrete and the continuous random vectors are treated.NEWLINENEWLINEThe characteristic functions and the moment-generating functions for random variables and vectors are introduced in Chapters 8 and 9, respectively. The expressions of the characteristic function are presented for most commonly used distributions. Also, the relationship between the moment-generating function and the characteristic function is discussed and the properties of both functions are provided.NEWLINENEWLINEChapter~10 describes the Gaussian random vectors that are extensiv…
description: scientific article; zbMATH DE number 6243671