
Introduction to Probability Theory
Description
Book Introduction
For those majoring in probability theory who require a broad knowledge of probability theory, all the theories, including methodological and theoretical aspects and basic mathematical calculations, are systematically organized.
In addition, it contains a variety of appropriate examples to help students develop their own probabilistic thinking and understand and deal with problems arising in real life using probabilistic methods. Practice problems are also evenly distributed from easy to difficult.
In particular, in order to understand probability theory using a mathematical tool called measure, the appendix aims to provide basic knowledge about the relationship between probability and measure from the perspective of measure theory.
Since the basic concepts of measures and measurable functions are necessary for understanding probability theory, the appendix will be of great help in studying the contents of the main text.
In addition, it contains a variety of appropriate examples to help students develop their own probabilistic thinking and understand and deal with problems arising in real life using probabilistic methods. Practice problems are also evenly distributed from easy to difficult.
In particular, in order to understand probability theory using a mathematical tool called measure, the appendix aims to provide basic knowledge about the relationship between probability and measure from the perspective of measure theory.
Since the basic concepts of measures and measurable functions are necessary for understanding probability theory, the appendix will be of great help in studying the contents of the main text.
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index
Chapter 01 Probability Space
1.
History of Probability 2
2.
Probability Space and Definition of Probability 6
3.
Conditional probability 21
4.
Independence Incident 31
Chapter 02 Random Variables and Distributions
1.
Random Variables and Distributions 38
2.
Discrete distribution 47
3.
Continuous distribution 57
4.
70 Various Continuous Distributions
Chapter 03 Moments and Generating Functions
1.
Momentum of random variable 80
2.
Generating function 92
3.
Moment Inequality of Random Variables 103
Chapter 04 Probability Vectors and Distributions
1.
Probability Vector 114
2.
Independence of Random Variables 133
3.
Functions of Probability Vectors 141
4.
Moments and Generating Functions of Probability Vectors 159
5.
Conditional Expectation and the Least Squares Principle 176
Chapter 05 Extreme Distributions
1.
Various convergence forms 194
2.
Laws of Large Numbers and the Central Limit Theorem 211
supplement
1.
Case 228
2.
Measure and Probability 235
3.
Decision Making Using Expected Value in Economic Phenomena 249
Probability distribution table 257
Practice Problem Answer 268
Reference 275
Search 276
1.
History of Probability 2
2.
Probability Space and Definition of Probability 6
3.
Conditional probability 21
4.
Independence Incident 31
Chapter 02 Random Variables and Distributions
1.
Random Variables and Distributions 38
2.
Discrete distribution 47
3.
Continuous distribution 57
4.
70 Various Continuous Distributions
Chapter 03 Moments and Generating Functions
1.
Momentum of random variable 80
2.
Generating function 92
3.
Moment Inequality of Random Variables 103
Chapter 04 Probability Vectors and Distributions
1.
Probability Vector 114
2.
Independence of Random Variables 133
3.
Functions of Probability Vectors 141
4.
Moments and Generating Functions of Probability Vectors 159
5.
Conditional Expectation and the Least Squares Principle 176
Chapter 05 Extreme Distributions
1.
Various convergence forms 194
2.
Laws of Large Numbers and the Central Limit Theorem 211
supplement
1.
Case 228
2.
Measure and Probability 235
3.
Decision Making Using Expected Value in Economic Phenomena 249
Probability distribution table 257
Practice Problem Answer 268
Reference 275
Search 276
GOODS SPECIFICS
- Date of issue: August 30, 2025
- Page count, weight, size: 286 pages | 188*257*20mm
- ISBN13: 9791160737790
- ISBN10: 1160737797
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