Titlebook: Probability Inequalities; Zhengyan Lin,Zhidong Bai Book 2011 Springer-Verlag Berlin Heidelberg 2011 Dependent random variables.Distributio

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7. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China..978-3-642-43777-9978-3-642-05261-3

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Elementary Inequalities of Probabilities of Events,In this Chapter, we shall introduce some basic inequalities which can be found in many basic textbooks on probability theory, such as (.), (.), etc.

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Inequalities Related to Commonly Used Distributions,Commonly used distributions play an important role in applied statistics, statistical computing and applied probability. So, inequalities related to these distributions are of great interest in these areas.

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Inequalities Related to Characteristic Functions,The characteristic function (c.f.) or Fourier transformation is an important mathematical tool in probability theory, especially in the theory of limiting theorems of sums of independent random variables. Most of the inequalities can be found in (.) and (.).

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Probability Inequalities of Random Variables,Probability inequalities of random variables, especially those of sums of random variables, play important roles in analytic probability theory, say, limiting theorems. Not only the applications of these inequalities, the proofs of these inequalities are also good illustrations of some important mathematical methodologies in probability theory.

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