描述
开 本: 16开纸 张: 胶版纸包 装: 平装是否套装: 否国际标准书号ISBN: 9787111482772丛书名: 华章数学原版精品系列
内容简介
概率论是研究自然界和人类社会中*现象数量规律的数学分支，本书通过大量的例子讲述了概率论的基础知识，主要内容有组合分析、概率论公理化、条件概率和独立性、离散和连续型*变量、*变量的联合分布、期望的性质、极限定理等。本书附有大量的练习，分为习题、理论习题和自检习题三大类，其中自检习题部分还给出全部解答。本书作为概率论的入门书，适用于大专院校数学、统计、工程和相关专业(包括计算科学、生物、社会科学和管理科学)的学生阅读，也可供应用工作者参考。
目 录
COMBINATORIAL ANALYSIS
1.1 Introduction
1.2 The Basic Principle of Counting
1.3 Permutations
1.4 Combinations
1.5 Multinomial Coefficients
1.6 The Number of Integer Solutions of Equations
AXIOMS OF PROBABILITY
Introduction
Sample Space and Events
Axioms of Probability
Some Simple Propositions
Sample Spaces Having Equally Likely
Outcomes
Probability as a Continuous Set Function
Probability as a Measure of Belief
CONDITIONAL PROBABILITY
AND INDEPENDENCE
3.1 Introduction
3.2 Conditional Probabilities
3.3 Bayes’s Formula
3.4 Independent Events
3.S P(F) Is a Probability
4 RANDOM VARIABLES
4.1 Random Variables it
4.2 Discrete Random Variables
4.3 Expected Value
4.4 Expectation of a Function of a Random
Variable
4.5 Variance
4.6 The Bernoulli and Binomial Random
Variables
4.7 The Poisson Random Variable
4.8 Other Discrete Probability Distributions
4.9 Expected Value of Sums of Random
Variables
4.10 Properties of the Cumulative Distribution
Function
CONTINUOUS RANDOM
VARIABLES
5.1 Introduction
5.2 Expectation and Variance of Continuous
Random Variables
5.3 The Uniform Random Variable
5.4 Normal Random Variables
5.5 Exponential Random Variables
5.6 Other Continuous Distributions
5.7 The Distribution of a Function
of a Random Variable
JOINTLY DISTRIBUTED RANDOM
VARIABLES
6.1 Joint Distribution Functions
6.2 Independent Random Variables
6.3 Sums of Independent Random
Variables
6.4 Conditional Distributions: Discrete
Case
6.5 Conditional Distributions: Continuous
Case
6.6 Order Statistics
6.7 Joint Probability Distribution of Functions
of Random Variables
6.8 Exchangeable Random Variables
PROPERTIES OF EXPECTATION
7.1 Introduction
7.2 Expectation of Sums of Random
Variables
7.3 Moments of the Number of Events that
Occur
7.4 Covariance, Variance of Sums, and
Correlations
7.S Conditional Expectation
7.6 Conditional Expectation and
Prediction
7.7 Moment Generating Functions
7.8 Additional Properties of Normal Random
Variables
7.9 General Definition of Expectation
LIMIT THEOREMS
8.1 Introduction
8.2 Chebyshev’s Inequality and the Weak
Law of Large Numbers
8.3 The Central Limit Theorem
8.4 The Strong Law of Large Numbers
8.5 Other Inequalities
8.6 Bounding the Error Probability When
Approximating a Sum of Independent
Bernoulli Random Variables by a Poisson
Random Variable
ADDITIONAL TOPICS
IN PROBABILITY
9.1 The Poisson Process
9.2 Markov Chains
9.3 Surprise, Uncertainty, and Entropy
9.4 Coding Theory and Entropy
SIMULATION
10.1 Introduction
10.2 General Techniques for Simulating
Continuous Random Variables
10.3 Simulating from Discrete Distributions
10.4 Variance Reduction Techniques
Answers to Selected Problems
Solutions to Self-Test Problems
and Exercises
Index
1.1 Introduction
1.2 The Basic Principle of Counting
1.3 Permutations
1.4 Combinations
1.5 Multinomial Coefficients
1.6 The Number of Integer Solutions of Equations
AXIOMS OF PROBABILITY
Introduction
Sample Space and Events
Axioms of Probability
Some Simple Propositions
Sample Spaces Having Equally Likely
Outcomes
Probability as a Continuous Set Function
Probability as a Measure of Belief
CONDITIONAL PROBABILITY
AND INDEPENDENCE
3.1 Introduction
3.2 Conditional Probabilities
3.3 Bayes’s Formula
3.4 Independent Events
3.S P(F) Is a Probability
4 RANDOM VARIABLES
4.1 Random Variables it
4.2 Discrete Random Variables
4.3 Expected Value
4.4 Expectation of a Function of a Random
Variable
4.5 Variance
4.6 The Bernoulli and Binomial Random
Variables
4.7 The Poisson Random Variable
4.8 Other Discrete Probability Distributions
4.9 Expected Value of Sums of Random
Variables
4.10 Properties of the Cumulative Distribution
Function
CONTINUOUS RANDOM
VARIABLES
5.1 Introduction
5.2 Expectation and Variance of Continuous
Random Variables
5.3 The Uniform Random Variable
5.4 Normal Random Variables
5.5 Exponential Random Variables
5.6 Other Continuous Distributions
5.7 The Distribution of a Function
of a Random Variable
JOINTLY DISTRIBUTED RANDOM
VARIABLES
6.1 Joint Distribution Functions
6.2 Independent Random Variables
6.3 Sums of Independent Random
Variables
6.4 Conditional Distributions: Discrete
Case
6.5 Conditional Distributions: Continuous
Case
6.6 Order Statistics
6.7 Joint Probability Distribution of Functions
of Random Variables
6.8 Exchangeable Random Variables
PROPERTIES OF EXPECTATION
7.1 Introduction
7.2 Expectation of Sums of Random
Variables
7.3 Moments of the Number of Events that
Occur
7.4 Covariance, Variance of Sums, and
Correlations
7.S Conditional Expectation
7.6 Conditional Expectation and
Prediction
7.7 Moment Generating Functions
7.8 Additional Properties of Normal Random
Variables
7.9 General Definition of Expectation
LIMIT THEOREMS
8.1 Introduction
8.2 Chebyshev’s Inequality and the Weak
Law of Large Numbers
8.3 The Central Limit Theorem
8.4 The Strong Law of Large Numbers
8.5 Other Inequalities
8.6 Bounding the Error Probability When
Approximating a Sum of Independent
Bernoulli Random Variables by a Poisson
Random Variable
ADDITIONAL TOPICS
IN PROBABILITY
9.1 The Poisson Process
9.2 Markov Chains
9.3 Surprise, Uncertainty, and Entropy
9.4 Coding Theory and Entropy
SIMULATION
10.1 Introduction
10.2 General Techniques for Simulating
Continuous Random Variables
10.3 Simulating from Discrete Distributions
10.4 Variance Reduction Techniques
Answers to Selected Problems
Solutions to Self-Test Problems
and Exercises
Index
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