The book consists of eight chapters, which covers the fundamentals of probability and statistics. In the first five chapters, that is, The Concepts of Probability, Random Variables and Distributions, Multivariate Distribution, Numerical Characteristics of Random Variables, Law of Large Numbers and Central Limit Theorems, we introduce some elementary probability concepts, indicate how probabilities
1 Probability of Events
1．1 Experiments and Events
1．2 Set Theory
1．3 Frequency and Probability
1．4 The Classical Probability
1．5 Geometrical Probability
1．6 Conditional Probability
1．7 Independence of Events
2 Random Variables and Distributions
2．1 Random Variables and Distribution Functions
2．2 Discrete Random Variables
2．3 Continuous Random Variables
2．4 Functions of a Random Variable
3 Multivariate Random Variables
3．1 Bivariate Random Variables
3．2 Marginal Distributions
3．3 Conditional Distributions
3．4 Independent Random Variables
3．5 Functions of Two or More Random Variables
3．6 Multivariate Distributions
4 Numerical Characteristics of Random Variables
4．1 Mathematical Expectation
4．2 Variance
4．3 Covariance and Correlation Coefficient
4．4 Moments
5 Law of Large Numbers and Central Limit Theorems
5．1 Law of Large Numbers
5．2 Central Limit Theorems
6 Random Samples and Sampling Distributions
6．1 Random Samples
6．2 Sampling Distributions
7 Parametric Estimation
7．1 Point Estimation
7．2 Evaluation of Estimators
7．3 Interval Estimation
8 Testing Hypotheses
8．1 Problems of Testing Hypotheses
8．2 Testing Hypotheses about Normal Distribution
8．3 P-value
9 Some background Materials
9．1 Permutations
9．2 k-Permutations
9．3 Combinations
Appendix 1 Table of Binomial Probabilities
Apperdix 2 Table of Poisson Probabilities
Appendix 3 Table of Standard Normal Distribution
Appendix 4 Table of the t Distribution
Appendix 5 Table of the X2 Distribution
Appendix 6 Table of the F Distribution
Appendix 7 Key to exercises
References
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