## Table of contents for Probability and statistical inference / Robert V. Hogg, Elliot A. Tanis.

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```1  Probability .................................                1
1.1 Basic Concepts ................        ...........      1
1.2 Properties of Probability ................... .....    11
1.3 Methods of Enumeration ................. ......        20
1.4  Conditional Probability  ..................     ......  29
1.5 Independent Events ................... ....... 38
1.6  Bayes's Theorem  ................... .........        45
2  Discrete Distributions ........................... 51
2.1 Random Variables of the Discrete Type . .............. 51
2.2 Mathematical Expectation . .................. ....     61
2.3 The Mean, Variance, and Standard Deviation . ...........  67
2.4 Bernoulli Trials and the Binomial Distribution ........... . 78
2.5 The Moment-Generating Function . .................     89
2.6 The Poisson Distribution ................... ..... 99
3  Continuous Distributions  ....................... 111
3.1  Continuous-Type Data . ..................      ...... 111
3.2 Exploratory Data Analysis . .................. .... 121
3.3 Random Variables of the Continuous Type . . . . . . . . . . . . . 131
3.4 The Uniform and Exponential Distributions ............. 141
3.5 The Gamma and Chi-Square Distributions . ............. 149
3.6  The Normal Distribution . ..................     ..... 157
3.7 Additional Models ........................... 168
4   nivariac iDistributions . . . . .                         .     79
4.1 Distributions of Two Random Variables ..... .......... 179
4.2  The Correlation Coefficient . .................. . . . 190
4.3  Conditional Distributions  .................. .       . . .  197
4.4  The Bivariate Normal Distribution . ................. 207
5   Distributions of Functions of Random Variables . . . ..    .  215
5.1 Functions of One Random Variable ..........    ........ 215
5.2  Transformations of Two Random Variables ............. 224
5.3  Several Independent Random Variables . .............. 234
5.4  The Moment-Generating Function Technique . ........... 242
5.5  Random Functions Associated with Normal Distributions ..... 246
5.6 The Central Limit Theorem ................... .. . 255
5.7  Approximations for Discrete Distributions . ............. 263
6   Estimation  ......   ............. . . . .         ..... ...  273
6.1  Point Estimation  ...................           .. . . . . .  273
6.2  Confidence Intervals for Means . .................. . 283
6.3  Confidence Intervals for the Difference of Two Means ....... 291
6.4  Confidence Intervals for Variances . ................. 302
6.5  Confidence Intervals for Proportions . ................ 307
6.6  Sample Size ................. ............ 314
6.7  A Simple Regression Problem ................... .. 321
6.8  More Regression  ...................           ......... 333
7   Tests of Statistical Hypotheses .... ...... .. .. .       .  ..... 343
7.1 Tests about Proportions . .................. ..... 343
7.2  Tests about One Mean ..................       . . . . . . .  353
7.3  Tests of the Equality of Two Means . ................. 363
7.4  Tests for Variances  . ..................        ........ 373
7.5  One-Factor Analysis of Variance . .................. 379
7.6  Two-Factor Analysis of Variance . .................. 389
7.7  Tests Concerning Regression and Correlation ............ 399
8   Noparamnietric Methods . . ................... .... 4. 07
8.1 Chi-Square Goodness-of-Fit Tests . .................. 407
8.2  Contingency Tables . ..................          ........ 417
8.3  Order Statistics  ................... .......... 428
8.4  Distribution-Free Confidence Intervals for Percentiles ....... 436
8.5  The Wilcoxon Tests ................... ....... 443
8.6  Run Test and Test for Randomness . ................. 455
8.7 Kolmogorov-Smirnov Goodness-of-Fit Test . ............ 461
8.8 Resampling Methods .......................... 467
9  Bayesian Methods ...... ......................... 477
9.1  Subjective Probability  ...................    ...... 477
9.2  Bayesian Estimation  . ..................     ....... 483
9.3 More Bayesian Concepts . .................. ..... 490
10   Some Theory ................................              497
10.1  Sufficient Statistics  . ..................  ........  497
10.2 Power of a Statistical Test ................... .... 505
10.3  Best Critical Regions . ..................   ....... 512
10.4 Likelihood Ratio Tests ........... ............. 519
10.5 Chebyshev's Inequality and Convergence in Probability ....... 525
10.6 Limiting Moment-Generating Functions . .............. 529
10.7 Asymptotic Distributions of Maximum Likelihood Estimators . . . 535
11   Quality Improvement through Statistical Methods ......... 541
11.1 Time Sequences ................   .... ..........541
11.2 Statistical Quality Control ........... ...... ...... 547
11.3 General Factorial and 2k Factorial Designs . . . . ........  . . 558
11.4 Understanding Variation ................... ..... 564
APPENDICES
A   References ................           .................571
B   Tables  ...   ......................          ......... ..573
C   Answers to Selected Odd-Numbered Exercises ........... 601
D   Review of Selected Mathematical Techniques ...... .CD-ROM

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Library of Congress subject headings for this publication: Probabilities, Mathematical statistics