Introduction to Mathematical Statistics

Cover......Page 1
Preface......Page 6
Contents......Page 8
1 Introduction......Page 14
References......Page 16
2.2 Sample Space......Page 17
2.3 Sample Space Probabilities......Page 18
2.4 Events......Page 19
2.5 Addition Theorem......Page 21
2.6 Multiplication Theorem......Page 23
2.7 Bayes' Formula......Page 28
2.8 Combinatorial Formulas......Page 30
2.10 Frequency Functions......Page 35
2.11 Joint Frequency Functions......Page 37
2.12 Marginal & Conditional Distributions......Page 40
2.13 Continuous Frequency Functions......Page 45
2.14 Joint Continuous Frequency Functions......Page 51
Exercises......Page 53
3.1 Mathematical Models......Page 58
3.2 Testing Hypotheses......Page 59
3.3 Estimation......Page 69
Exercises......Page 74
4.1 Introduction......Page 77
4.2 Classification of Data......Page 78
4.3 Graphical Representation of Empirical Distributions......Page 80
4.4 Arithmetical Representation of Empirical Distributions......Page 82
Exercises......Page 92
5.2 Discrete Variables......Page 95
5.3 Continuous Variables......Page 108
5.4 Other Distributions......Page 129
References......Page 136
Exercises......Page 137
6.1 Random Sampling......Page 144
6.2 Moments of Multivariate Distributions......Page 146
6.3 Properties of E......Page 148
6.5 Distribution of × From A Normal Distribution......Page 151
6.6 Distribution of × From Non-Normal Distributions......Page 156
6.7 Distribution of the Difference of Two Means......Page 159
6.8 Distribution of the Difference of Two Proportions......Page 161
6.9 Chi-Square Distribution......Page 164
Exercises......Page 168
7.1 Linear Correlation......Page 173
7.2 Linear Regression......Page 181
7.3 Multiple Linear Regression......Page 185
7.4 Curvilinear Regression......Page 188
7.5 Linear Discriminant Functions......Page 192
References......Page 197
Exercises......Page 198
8.1 Continuous Distributions of Two Variables......Page 202
8.2 Normal Distribution of Two Variables......Page 210
8.3 Normal Correlation......Page 216
8.4 Normal Regression......Page 218
References......Page 221
Exercises......Page 222
9.1 Testing Hypotheses......Page 225
9.2 Estimation......Page 241
Exercises......Page 253
10.1 The χ² Test......Page 257
10.2 Limitations of the χ² Test......Page 260
10.3 Applications......Page 261
10.4 Generality of the χ² Test......Page 262
10.5 Frequency Curve Fitting......Page 263
10.6 Contingency Tables......Page 265
10.7 Indices of Dispersion......Page 268
References......Page 271
Exercises......Page 272
11.1 Distribution of A Function of Random Variables......Page 275
11.2 The χ² Distribution......Page 279
11.3 Applications of the χ² Distribution......Page 281
11.4 Student's T Distribution......Page 284
11.5 Applications of the T Distribution......Page 288
11.6 The F Distribution......Page 296
11.7 Applications of the F Distribution......Page 298
11.8 Distribution of the Range......Page 301
11.9 Applications of the Range......Page 304
References......Page 305
Exercises......Page 306
12.1 Randomization, Replication, & Sensitivity......Page 310
12.2 Analysis of Variance......Page 312
12.3 Stratified Sampling......Page 328
12.4 Sampling Inspection......Page 331
Exercises......Page 338
13 Nonparametric Methods......Page 342
13.1 Sign Test......Page 343
13.2 Rank Sum Test......Page 346
13.3 Runs......Page 348
13.4 Serial Correlation......Page 354
13.5 Kolmogorov-Smirnov Statistic......Page 358
Exercises......Page 362
14.1 Sequential Analysis......Page 365
14.2 Multiple Classification Techniques......Page 375
14.3 Bayes Techniques......Page 380
References......Page 385
Exercises......Page 386
1 Properties of r......Page 388
2 Likelihood Ratio Test for Goodness of Fit......Page 389
3 Cramer-Rao Inequality......Page 392
4 Transformations & Jacobians......Page 394
5 Independence of × & s² for Normal Distributions......Page 396
Tables......Page 400
Answers to Odd-Numbered Exercises......Page 426
Index......Page 438