概率论与数理统计

1Probability of Events1
1.1Experiments and Events 1
1.2Set Theory3
1.3Frequency and Probability6
1.4The Classical Probability9
1.5Geometrical Probability12
1.6Conditional Probability13
1.7Independence of Events20 2Random Variables and Distributions27
2.1Random Variables and Distribution Functions27
2.2Discrete Random Variables31
2.3Continuous Random Variables39
2.4Functions of a Random Variable47 3Multivariate Random Variables53
3.1Bivariate Random Variables53
3.2Marginal Distributions59
3.3Conditional Distributions61
3.4Independent Random Variables64
3.5Functions of Two or More Random Variables66
3.6Multivariate Distributions72 4Numerical Characteristics of Random Variables76
4.1Mathematical Expectation76
4.2Variance81
4.3Covariance and Correlation Coefficient84
4.4Moments87 5Law of Large Numbers and Central Limit Theorems91
5.1Law of Large Numbers91
5.2Central Limit Theorems95 6Random Samples and Sampling Distributions99
6.1Random Samples99
6.2Sampling Distributions101 7Parametric Estimation113
7.1Point Estimation113
7.2Evaluation of Estimators117
7.3Interval Estimation121 8Testing Hypotheses130
8.1Problems of Testing Hypotheses130
8.2Testing Hypotheses about Normal Distribution134
8.3Pvalue146 9Some background Materials157
9.1Permutations157
9.2kPermutations160
9.3Combinations163 Appendix 1Table of Binomial Probabilities168
Apperdix 2Table of Poisson Probabilities171
Appendix 3Table of Standard Normal Distribution174
Appendix 4Table of the t Distribution176
Appendix 5Table of the 2 Distribution178
Appendix 6Table of the F Distribution181
Appendix 7Key to exercises189 References199