The natural axiom system of probability theory : mathematical model of the random universe / Daguo Xiong ; translated from Chinese by Wu Jian.

Format:

Book

Author/Creator:

Xiong, Daguo.

Language:

Chinese

English

Subjects (All):

Probabilities.

Axioms.

Random variables.

Physical Description:

1 online resource (xiv, 184 p.)

Edition:

1st ed.

Place of Publication:

River Edge, N.J. : World Scientific, 2003.

Language Note:

English

Summary:

The causation space established in this book 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 book also points out that the basic unit to be studied in the probability theory is the random test, and not a stand-alone event.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

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

ISBN:

9786611935566

9781281935564

1281935565

9789812795137

9812795138

OCLC:

815752508