Probability and Statistical Inference

Robert Bartoszynski, Magdalena Niewiadomska-Bugaj9780471696933, 0471696935

Probability and Statistical Inference, Second Edition is a user-friendly book that stresses the comprehension of concepts instead of the simple acquisition of a skill or tool. It provides a mathematical framework that permits students to carry out various procedures using any number of computer software packages as opposed to relying on one particular package. Its unique approach to problems allows readers to integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.

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Table of contents :
PROBABILITY AND STATISTICAL INFERENCE……Page 6
CONTENTS……Page 8
Preface……Page 13
1.1 Introduction……Page 16
1.2 Sample Space……Page 17
1.3 Algebra of Events……Page 24
1.4 Infinite Operations on Events……Page 31
2.2 Probability as a Frequency……Page 40
2.3 Axioms of Probability……Page 41
2.4 Consequences of the Axioms……Page 46
2.5 Classical Probability……Page 51
2.6 Necessity of the Axioms……Page 52
2.7 Subjective Probability……Page 57
3.2 Product Sets, Orderings, and Permutations……Page 62
3.3 Binomial Coefficients……Page 70
3.4 Extension of Newton’s Formula……Page 83
3.5 Multinomial Coefficients……Page 84
4.1 Introduction……Page 88
4.2 Conditional Probability……Page 89
4.3 Partitions; Total Probability Formula……Page 95
4.4 Bayes’ Formula……Page 102
4.5 Independence……Page 107
4.6 Exchangeability; Conditional Independence……Page 114
5.1 Introduction and Basic Definitions……Page 118
5.2 Definition of a Markov Chain……Page 121
5.3 n-Step Transition Probabilities……Page 126
5.4 The Ergodic Theorem……Page 129
5.5 Absorption Probabilities……Page 137
6.1 Introduction……Page 140
6.2 Distributions of Random Variables……Page 141
6.3 Discrete and Continuous Random Variables……Page 154
6.4 Functions of Random Variables……Page 165
6.5 Survival and Hazard Functions……Page 172
7.1 Bivariate Distributions……Page 176
7.2 Marginal Distributions; Independence……Page 183
7.3 Conditional Distributions……Page 195
7.4 Bivariate Transformations……Page 202
7.5 Multidimensional Distributions……Page 211
8.1 Introduction……Page 218
8.2 Expected Value……Page 219
8.3 Expectation as an Integral……Page 227
8.4 Properties of Expectation……Page 235
8.5 Moments……Page 243
8.6 Variance……Page 251
8.7 Conditional Expectation……Page 263
8.8 Inequalities……Page 267
9.1 Bernoulli Trials and Related Distributions……Page 272
9.2 Hypergeometric Distribution……Page 285
9.3 Poisson Distribution and Poisson Process……Page 291
9.4 Exponential, Gamma and Related Distributions……Page 305
9.5 Normal Distribution……Page 311
9.6 Beta Distribution……Page 321
10.1 Statistics and their Distributions……Page 326
10.2 Distributions Related to Normal……Page 328
10.3 Order Statistics……Page 334
10.4 Generating Random Samples……Page 340
11.5 Sampling……Page 345
10.6 Central Limit Theorem……Page 357
11.1 Overview……Page 366
11.2 Descriptive Statistics……Page 368
11.3 Basic Model……Page 373
11.4 Bayesian Statistics……Page 375
11.6 Measurement Scales……Page 382
12.1 Introduction……Page 388
12.2 Consistency……Page 393
12.3 Loss, Risk, and Admissibility……Page 396
12.4 Efficiency……Page 401
12.5 Methods of Obtaining Estimators……Page 409
12.6 Sufficiency……Page 439
12.7 Interval Estimation……Page 455
13.1 Introduction……Page 470
13.2 Intuitive Background……Page 475
13.3 Most Powerful Tests……Page 484
13.4 Uniformly Most Powerful Tests……Page 496
13.5 Unbiased Tests……Page 502
13.6 Generalized Likelihood Ratio Tests……Page 506
13.7 Conditional Tests……Page 513
13.8 Tests and Confidence Intervals……Page 516
13.9 Review of Tests for Normal Distributions……Page 517
13.10 Monte Carlo, Bootstrap, and Permutation Tests……Page 527
14.1 Introduction……Page 532
14.2 Regression of the First and Second Kind……Page 534
14.3 Distributional Assumptions……Page 540
14.4 Linear Regression in the Normal Case……Page 543
14.5 Testing Linearity……Page 550
14.6 Prediction……Page 553
14.7 Inverse Regression……Page 555
14.8 BLUE……Page 557
14.9 Regression Toward the Mean……Page 560
14.10 Analysis of Variance……Page 561
14.11 One-way Layout……Page 562
14.12 Two-way Layout……Page 565
14.13 ANOVA Models with Interaction……Page 568
14.14 Further Extensions……Page 572
15.1 Introduction……Page 574
15.2 Glivenko-Cantelli Theorem……Page 575
15.3 Kolmogorov-Smirnov Tests……Page 579
15.4 One-Sample Rank Tests……Page 586
15.5 Two-Sample Rank Tests……Page 593
15.6 Kruskal-Wallis Test……Page 597
16.1 Introduction……Page 600
16.2 Chi-square Tests……Page 602
16.3 Homogeneity and Independence……Page 608
16.4 Consistency and Power……Page 614
16.5 2×2 Contingency Tables……Page 619
16.6 r × c Contingency Tables……Page 627
Statistical Tables……Page 632
Bibliography……Page 644
Answers to Odd-Numbered Problems……Page 649
Index……Page 657