عنوان

The natural axiom system of probability theory :

1281935565

9781281935564

9789812795137

9812795138

9812384081

b750728

The natural axiom system of probability theory :

[Book]

mathematical model of the random universe /

Daguo Xiong ; translated from Chinese by Wu Jian.

River Edge, N.J. :

World Scientific,

2003.

1 online resource (xiv, 184 pages)

Includes bibliographical references (pages 177-178) and index.

Preliminary -- 1. Real background of probability theory. 1.1. Research object. 1.2. Research task. 1.3. Probability -- 2. Natural axiom system of probability theory. 2.1. Element of probability theory and six groups of axioms. 2.2. The first group of axioms: the group of axioms of event space. 2.3. The second group of axioms: the group of axioms of causal space. 2.4. The third group of axioms: the group of axioms of random test. 2.5. Several kinds of typical random tests. 2.6. Joint random tests. 2.7. The forth group of axioms: the group of axioms of probability measure. 2.8. Point functions on random test. 2.9. The fifth group of axioms: the group of axioms of conditional probability measure. 2.10. Point functions on random test (continued). 2.11. The sixth group of axioms: the group of axioms of probability modelling -- 3. Introduction of random variables. 3.1. Intuitive background of random variables. 3.2. Basic conceptions of random variable. 3.3. Basic conceptions of random vector. 3.4. Basic conceptions of broad stochastic process.

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The causation space established in this text is a mathematical model of the random universe and a "living house" of all random tests and probability spaces. By using this space, one can introduce the mathematical calculation methods related to probability spaces and random tests. The work also points out that the basic unit to be studied in the probability theory is the random test, and not a stand-alone event.

Natural axiom system of probability theory.

9789812384089

Axioms.

Probabilities.

Random variables.

Axioms.

MATHEMATICS-- Probability & Statistics-- General.

Probabilities.

Random variables.

MAT-- 029000

PBT

Xiong, Daguo.

20201204102713.0

pn

[Book]

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