概率論

前言

The subject matter of probability theory is the mathematical analysis of random events, that is, of those empirical phenomena which do not have deterministic regularity but possess some statistical regularity.　Probability theory, as science, originated in the middle of the seventeenth century with Pascal, Fermat and Huygens, although special calculations of probabilities in games of chance had been made earlier. The real history of probability theory begins with the work of James Bernoulli, Ars Conjectandi (The Art of Guessing) published .

內(nèi)容概要

　　《概率論(英漢對(duì)照版)》以英文的形式介紹了高等學(xué)校概率論方面的知識(shí)。The subject matter of
probability theory is the mathematical analysis of random events,
that is, of those empirical phenomena which do not have
deterministic regularity but possess some statistical
regularity.

書籍目錄

chapter 1 events and probabilities
1.1 random phenomena and statistical regularity
1.1.1 random phenomena
1.1.2 the statistical definition of probability
1.2 classical probability models
1.2.1 sample points and sample spaces
1.2.2 classical probability models
1.2.3 geometric probability models
1.3 the axiomatic definition of probability
1.3.1 events
1.3.2 probability space
1.3.3 continuity of probability measure
1.4 conditional probability and independent events
1.4.1 conditional probability
1.4.2 total probability formula and bayes’rule
1.4.3 independent events
chapter 2 random variables and distribution functions
2.1 discrete random variables
2.1.1 the concept of random variables
2.1.2 discrete random variables
2.2 distribution functions and continuous random variables
2.2.1 distribution functions
2.2.2 continuous random variables and density functions
2.2.3 typical continuous random variables
2.3 random vectors
2.3.1 discrete random vectors
2.3.2 joint distribution functions
2.3.3 continuous random vectors
2.4 conditional distributions and independence
2.4.1 conditional distributions
2.4.2 i ndependence of random variables
2.5 functions of random variables
2.5.1 functions of discrete random variables
2.5.2 functions of continuous random variables
2.5.3 functions of continuous random vectors
2.5.4 transforms of random vectors
2.5.5 important distributions in statistics
chapter 3 numerical characteristics and characteristic
functions
3.1 mathematical expectations
3.1.1 expectations for discrete random variables
3.1.2 expectations of continuous random variables
chapter 4 probability limit theorems
appendix a distribution of typical random variables
appendix b tables
index

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