Elements of Probability and Statistics(概率论与数理统计初步)

Chapter 1 Classical Probability 1 1.1 Sample Space 2 1.2 Event 4 1.3 Counting Sample Points 6 1.3.1 Multiplication Rule 6 1.3.2 Permutations and Combinations 7 1.4 The Concept of Probability 9 1.5 The Axioms of Probability 10 1.6 Some Element Properties on Probability 11 1.7 Assignment of Probabilities 12 1.8 Calculating Probabilities for Unions and Complements 14 1.9 Conditional Probability 16 1.10 Independence 19 1.11 The Law of Total Probability 21 1.12 Bayes Rule 22 Exercises 23 Chapter 2 Discrete Random Variables 28 2.1 Random Variables 28 2.2 Discrete Probability Distribution 29 2.3 Distribution Functions for Random Variables 30 2.4 Expected Values 32 2.5 Functions of a Random Variable 32 2.6 Variance and Standard Deviation 33 Exercises 34 Chapter 3 Continuous Random Variables 37 3.1 Distribution Functions for Continuous Random Variables 38 3.2 Expected Values 39 3.3 Variance 40 3.4 Properties of Expected Values and Variances 41 Exercises 41 Chapter 4 Examples of Random Variables 43 4.1 Binomial Distribution 43 4.2 Properties of Binomial Distributions 44 4.3 Poisson Distributions 44 4.4 The Normal Distribution 45 4.5 Relationships Between Binomial and Normal Distributions 46 Exercises 47 Chapter 5 Descriptive Statistics 50 5.1 Measures of Central Tendency 50 5.2 Measures of Dispersion 52 5.3 StemandLeaf Plot 52 Exercises 54 Chapter 6 Sampling Theory 56 6.1 Sampling 56 6.2 Random Samples, Random Numbers 57 6.3 Population Parameters 57 6.4 Sample Statistics 58 6.5 Sampling Distributions 59 6.6 The Sample Mean 59 6.7 Sampling Distribution of Means 60 6.8 Sampling Distribution of Proportions 61 6.9 Sampling Distribution of Differences and Sums 62 6.10 The Sample Variance 63 Exercises 63 Chapter 7 Estimation 65 7.1 Unbiased Estimates and Efficient Estimates 65 7.2 Point Estimates and Interval Estimates 66 7.3 Method of Moments 66 7.4 Maximum Likelihood Estimators 67 7.5 Confidence Interval Estimates of Population Parameters 70 Exercises 71 Chapter 8 Hypothesis Test 73 8.1 Statistical Hypothesis 73 8.2 Tests of Hypothesis 74 8.3 Type Ⅰ and Type Ⅱ Errors and Level of Significance 75 8.4 Simple and Composite Hypotheses 77 8.5 Testing Hypotheses about the Mean of a Normal Distribution with Known Variance 77 8.6 P Value 79 Exercises 81 Bibliography 82