Probability & statistics

Preface......Page 10
PART ONE:PROBABILITY......Page 12
1-1 Introduction......Page 14
1-2 The Four Interpretations of Probability......Page 20
2-1 Set Theory......Page 30
2-2 Probability Space......Page 40
2-3 Conditional Probability and Independence......Page 56
Problems......Page 67
3-1 Dual Meaning of Repeated Trials......Page 70
3-2 Bernoulli Trials......Page 75
3-3 Asymptotic Theorems......Page 81
3-4 Rare Events and Poisson Points......Page 88
Problems......Page 92
4-1 Introduction......Page 95
4-2 The Distribution Function......Page 99
4-3 Illustrations......Page 112
4-4 Functions of One Random Variable......Page 123
4-5 Mean and Variance......Page 132
Problems......Page 142
5-1 The Joint Distribution Function......Page 146
5-2 Mean, Correlation, Moments......Page 155
5-3 Functions of Two Random Variables......Page 166
Problems......Page 176
6-1 Conditional Distributions......Page 179
6-2 Bayes' Formulas......Page 185
6-3 Nonlinear Regression and Prediction......Page 192
6-4 System Reliability......Page 197
Problems......Page 206
7-1 General Concepts......Page 208
7-2 Applications......Page 215
7-3 Central Limit Theorem......Page 225
7-4 Special Distributions of Statistics......Page 230
Appendix: Chi-Square Quadratic Forms......Page 237
Problems......Page 240
PART TWO:STATISTICS......Page 244
8-1 Introduction......Page 246
8-2 The Major Areas of Statistics......Page 249
8-3 Random Numbers and Computer Simulation......Page 262
9-1 General Concepts......Page 284
9-2 Expected Values......Page 286
9-3 Variance and Correlation......Page 304
9-4 Percentiles and Distributions......Page 308
9-5 Moments and Maximum Likelihood......Page 312
9-6 Best Estimators and the Rao-Cramer Bound......Page 318
Problems......Page 327
10-1 General Concepts......Page 332
10-2 Basic Applications......Page 335
10-3 Quality Control......Page 353
10-4 Goodness-of-Fit Testing......Page 359
10-5 Analysis of Variance......Page 371
10-6 Neyman-Pearson, Sequential, and Likelihood Ratio Tests......Page 380
Problems......Page 393
11-1 Introduction......Page 399
11-2 Deterministic Interpretation......Page 402
11-3 Statistical Interpretation......Page 413
11-4 Prediction......Page 418
Problems......Page 422
12-1 Entropy of Partitions and Random Variables......Page 425
12-2 Maximum Entropy and Statistics......Page 433
12-3 Typical Sequences and Relative Frequency......Page 441
Problems......Page 446
Tables......Page 448
Answers and Hints for Selected Problems......Page 454
Index......Page 459