The Elements of Probability Theory and Some of Its ApplicationsPDF电子书下载

Part Ⅰ FOUNDATIONS 9

Chapter 1．Historical Introduction 11

1．Origin of mathematical probability theory． 11

2．Probability and experience． 13

3．Defects of the classical definition． 14

4．Generalization of the probability concept． 16

5．Applications． 18

6．Critical revision of foundations． 19

Chapter 2．Definition of Mathematical Probability 21

1．Mathematical models． 21

2．Random experiments． 22

3．Frequency ratios and mathematical probabilities． 26

Chapter 3．Elementary Rules of Calculation for Probabilities 29

1．Some simple properties of mathematical probability． 29

2．The addition rule． 30

3．Three fundamental propositions． 33

4．Conditional probabilities and the multiplication rule． 35

5．Independent events． 37

6．Bayes＇ theorem． 38

7．Problems． 40

Chapter 4．Some Applications of the Fundamental Theorems 42

1．Repeated observations． 42

2．Drawings with and without replacement． 45

3．Some further problems on games of chance． 49

4．Problems． 52

Part Ⅱ RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 55

Chapter 5．Variables and Distributions in One Dimension 57

1．Introduction． 57

2．Discrete distributions． 59

3．Continuous distributions． 61

4．Joint distributions of several variables． 65

5．Mean values． 71

6．Moments． 74

7．Location,dispersion,skewness． 76

8．Tchebycheff＇s theorem． 81

9．Addition of independent variables． 82

10．Generating functions． 84

11．Problems． 87

Chapter 6．The Binomial and Related Distributions 90

1．One and two point distributions． 90

2．The binomial distribution． 90

3．Bernoulli＇s theorem． 93

4．De Moivre＇s theorem． 69

5．The Poisson distribution． 102

6．Problems． 107

Chapter 7．The Normal Distribution 108

1．The normal functions． 108

2．The normal distribution． 110

3．Addition of independent normal variables． 113

4．The central limit theorem． 114

5．Asymptotic expansion derived from the normal distribution． 116

6．Transformed normal distributions． 118

7．The importance of the normal distribution for the applications． 120

8．Problems． 120

Chapter 8．Further Continuous Distributions 121

1．The X2 distribution． 121

2．The t distribution． 124

3．The F distribution． 127

4．The Pearson system． 127

5．Problems． 128

Chapter 9．Variables and Distributions in Two Dimensions 129

1．Moments and correlation coefficients． 129

2．Least squares regression． 133

3．Conditional distributions．The regression of the mean． 136

4．The normal distribution． 140

5．Problems． 144

Chapter 10．Variables and Distributions in More than Two Dimensions 145

1．Regression． 145

2．Partial correlation． 148

3．Multiple correlation． 150

4．The normal distribution． 151

5．Problems． 151

Part Ⅲ APPLICATIONS 153

Chapter 11．Introduction 155

1．Probability theory and statistical experience． 155

2．Applications of probability theory．Description． 157

3．Analysis． 158

4．Prediction． 159

Chapter 12．Descriptive Treatment of a Statistical Material 160

1．Tabulation and grouping． 160

2．The sample values and their distribution． 164

3．Graphical representation． 166

4．The characteristics of the sample． 171

5．Numerical computation of characteristics． 173

Chapter 13．Sampling Distributions 181

1．The characteristics as random variables． 181

2．The moments of the characteristics． 182

3．Asymptotic sampling distributions． 183

4．Exact sampling distributions． 184

5．Problems． 189

Chapter 14．Problems of Statistical Inference 190

1．Introduction． 190

2．Properties of estimates． 191

3．Methods of estimation． 194

4．Confidence intervals,I． 198

5．Confidence intervals．II． 207

6．General remarks on the testing of statistical hypotheses． 211

7．Problems． 213

Chapter 15．The X2 Test 215

1．The case of a completely specified hypothetical distribution． 215

2．The case when certain parameters are estimated from the sample． 220

3．Problems． 226

Chapter 16．Some Further Applications 228

1．Theory of errors,I．Direct observations． 228

2．Theory of errors,II．Indirect observations． 235

3．Regression problems． 242

4．Analysis of variance． 246

5．Sampling． 253

6．Statistical quality control． 257

7．Problems 260

Appendix 263

References 265

Solutions of Problems 266

Tables 273

Index 279