Introduction to Probability and Mathematical Statistics

TOC......Page 5
toc2......Page 6
Preface......Page 11
1.1 Introduction......Page 13
1.2 Notation and terminology......Page 14
1.3 Definition of probability......Page 21
1.4 Some properties of probability......Page 25
1.5 Conditional probability......Page 28
1.6 Counting techniques......Page 43
Exercises......Page 55
2.1 Introduction......Page 65
2.2 Discrete random variables......Page 68
2.3 Continuous random variables......Page 74
2.4 Some properties of expected values......Page 83
2.5 Moment generating functions......Page 90
Exercises......Page 95
3.1 Introduction......Page 102
3.2 Special discrete distributions......Page 103
3.3 Special continuous distributions......Page 121
3.4 Location and scale parameters......Page 136
Summary......Page 139
Exercises......Page 140
4.1 Introduction......Page 148
4.2 Joint discrete distributions......Page 149
4.3 Joint continuous distributions......Page 156
4.4 Independent random variables......Page 161
4.5 Conditional distributions......Page 165
4.6 Random samples......Page 170
Exercises......Page 177
5.1 Introduction......Page 183
5.2 Properties of expected values......Page 184
5.3 Correlation......Page 189
5.4 Conditional expectation......Page 192
5.5 Joint moment generating functions......Page 198
Summary......Page 200
Exercises......Page 201
6.1 Introduction......Page 205
6.2 The CDF technique......Page 206
6.3 Transformation methods......Page 209
6.4 Sums of random variables......Page 221
6.5 Order statistics......Page 226
Exercises......Page 238
7.1 Introduction......Page 243
7.2 Sequences of random variables......Page 244
7.3 The central limit theorem......Page 248
7.4 Approximations for the binomial distribution......Page 252
7.5 Asymptotic normal distributions......Page 255
7.6 Properties of stochastic convergence......Page 257
7.7 Additional limit theorems......Page 259
7.8 Asymptotic distributions of extreme-order statistics......Page 262
Exercises......Page 271
8.2 Statistics......Page 275
8.3 Sampling distributions......Page 279
8.4 The t, F, and beta distributions......Page 285
8.5 Large-sample approximations......Page 292
Exercises......Page 295
9.1 Introduction......Page 300
9.2 Some methods of estimation......Page 302
9.3 Criteria for evaluating estimators......Page 314
9.4 Large-sample properties......Page 323
9.5 Bayes and minimax estimators......Page 331
Summary......Page 339
Exercises......Page 340
10.1 Introduction......Page 347
10.2 Sufficient statistics......Page 349
10.3 Further properties of sufficient statistics......Page 354
10.4 Completeness and exponential class......Page 357
Exercises......Page 365
11.1 Introduction......Page 370
11.2 Confidence intervals......Page 371
11.3 Pivotal quantity method......Page 374
11.4 General method......Page 381
11.5 Two-sample problems......Page 389
11.6 Bayesian interval estimation......Page 394
Summary......Page 395
Exercises......Page 396
12.1 Introduction......Page 401
12.2 Composite hypotheses......Page 407
12.3 Tests for the normal distribution......Page 410
12.4 Binomial tests......Page 416
12.6 Most powerful tests......Page 418
12.7 Uniformly most powerful tests......Page 423
12.8 Generalized likelihood ratio tests......Page 429
12.9 Conditional tests......Page 438
12.10 Sequential tests......Page 440
Summary......Page 447
Exercises......Page 448
13.1 Introduction......Page 454
13.2 One-sample binomial case......Page 455
13.3 r-Sample binomial test (completely specified H0)......Page 456
13.4 One-sample multinomial......Page 459
13.5 r-Sample multinomial......Page 460
13.6 Test for independence, r x c contingency table......Page 462
13.7 Chi-squared goodness-of-fit test......Page 465
13.8 Other goodness-of-fit tests......Page 469
Summary......Page 473
Exercises......Page 474
14.1 Introduction......Page 480
14.2 One-sample sign test......Page 481
14.3 Binomial test (test on quantiles)......Page 483
14.4 Two-sample sign test......Page 488
14.5 Wilcoxon paired-sample signed-rank test......Page 489
14.6 Paired-sample randomization test......Page 494
14.7 Wilcoxon and Mann-Whitney (WMW) tests......Page 495
14.8 Correlation teststests of independence......Page 498
14.9 Wald-Wolfowjtz runs test......Page 504
Summary......Page 506
Exercises......Page 507
15.1 Introduction......Page 511
15.2 Linear regression......Page 512
15.3 Simple linear regression......Page 513
15.4 General linear model......Page 527
15.5 Analysis of hivariate data......Page 541
Summary......Page 546
Exercises......Page 547
16.1 Introduction......Page 552
16.2 Reliability concepts......Page 553
16.3 Exponential distribution......Page 560
16.4 Weibull distribution......Page 572
16.5 Repairable systems......Page 582
Exercises......Page 591
APPENDIX A -- REVIEW OF SETS......Page 599
APPENDIX B -- SPECIAL DISTRIBUTION......Page 606
APPENDIX C -- TABLES OF DISTRIBUTION......Page 610
ANSWERS TO SELECTED EXERCISE......Page 631
REFERENCE......Page 650
INDEX......Page 653