Foundations of probability and statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Forth Worth u.a.
Saunders College Publ.
1993
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung graph. Darst. |
| ISBN: | 0030718066 |
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Record in the Search Index
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| adam_text | FOUNDATIONS OF PROBABILITY AND STATISTICS WILLIAM C. RINAMAN LE MOYNE
COLLEGE SYRACUSE, NEW YORK SAUNDERS COLLEGE PUBLISHING HARCOURT BRACE
COLLEGE PUBLISHERS FORT WORTH PHILADELPHIA SAN DIEGO NEW YORK ORLANDO
AUSTIN SAN ANTONIO TORONTO MONTREAL LONDON SYDNEY TOKYO TABLE OF
CONTENTS CHAPTER 1 RANDOM EXPERIMENTS AND PROBABILITY 1 1.1 INTRODUCTION
1 1.2 SET THEORY 3 1.3 RANDOM EXPERIMENTS 12 1.4 THE AXIOMS OF
PROBABILITY 17 1.5 COUNTING ELEMENTARY EVENTS 27 1.6 PROBABILITIES FOR
FINITE SAMPLE SPACES WITH EQUALLY LIKELY OUTCOMES 41 CHAPTER SUMMARY 53
REVIEW EXERCISES 56 CHAPTER 2 CONDITIONAL PROBABILITY AND INDEPENDENCE
59 2.1 INTRODUCTION 59 2.2 CONDITIONAL PROBABILITY 61 2.3 BAYES RULE 71
2.4 INDEPENDENCE 77 CHAPTER SUMMARY 92 REVIEW EXERCISES 92 CHAPTER 3
RANDOM VARIABLES 95 3.1 INTRODUCTION 95 VUE 3.2 THE DISTRIBUTION FUNCTION
99 VIII TABLE OF CONTENTS 3.3 DISCRETE RANDOM VARIABLES 108 3.4
CONTINUOUS RANDOM VARIABLES 114 3.5 RANDOM VECTORS 121 3.6 INDEPENDENT
RANDOM VARIABLES 139 3.7 CONDITIONAL DISTRIBUTIONS 145 CHAPTER SUMMARY
149 REVIEW EXERCISES 152 CHAPTER 4 EXPECTATION 155 4.1 INTRODUCTION 155
4.2 EXPECTED VALUE 156 4.3 EXPECTATION OF A FUNCTION OF A RANDOM
VARIABLE 162 4.4 MOMENTS 173 4.5 MOMENT GENERATING FUNCTIONS 189 4.6
CONDITIONAL EXPECTATION 197 CHAPTER SUMMARY 203 REVIEW EXERCISES 204
CHAPTER 5 PROBABILITY DISTRIBUTIONS 207 5.1 INTRODUCTION 207 5.2
HYPERGEOMETRIC DISTRIBUTION 208 5.3 DISTRIBUTIONS BASED ON INDEPENDENT
BERNOULLI TRIALS 211 5.4 MULTINOMIAL DISTRIBUTION 218 5.5 POISSON
DISTRIBUTION 223 5.6 UNIFORM DISTRIBUTION 228 5.7 NORMAL DISTRIBUTION
232 5.8 GAMMA DISTRIBUTION 239 5.9 OTHER CONTINUOUS DISTRIBUTIONS 244
5.9.1 WEIBULL DISTRIBUTION 244 5.9.2 BETA DISTRIBUTION 245 5.9.3 CAUCHY
DISTRIBUTION 246 5.9.4 DOUBLE EXPONENTIAL DISTRIBUTION 247 5.9.5
LOGISTIC DISTRIBUTION 248 5.10 BIVARIATE NORMAL DISTRIBUTION 250 TABLE
OF CONTENTS IX CHAPTER SUMMARY 253 REVIEW EXERCISES 254 CHAPTER 6
DISTRIBUTIONS OF FUNCTIONS OF RANDOM VARIABLES 257 6.1 INTRODUCTION 257
6.2 TRANSFORMATIONS OF DISCRETE RANDOM VARIABLES 257 6.3 THE
DISTRIBUTION FUNCTION METHOD 262 6.4 THE TRANSFORMATION OF VARIABLES
METHOD 265 6.5 MOMENT GENERATING FUNCTION METHOD 270 6.6 SUMS OF
INDEPENDENT RANDOM VARIABLES 274 6.7 DISTRIBUTION OF FUNCTIONS OF
SEVERAL RANDOM VARIABLES 277 CHAPTER SUMMARY 286 REVIEW EXERCISES 288
CHAPTER 7 LIMIT THEOREMS 291 7.1 INTRODUCTION 291 7.2 CONVERGENCE IN
PROBABILITY 292 7.3 CENTRAL LIMIT THEOREM 308 7.4 MORE ON CONVERGENCE IN
DISTRIBUTION 315 CHAPTER SUMMARY 319 REVIEW EXERCISES 322 CHAPTER 8
STATISTICAL MODELS 325 8.1 INTRODUCTION 325 8.2 POPULATIONS AND RANDOM
SAMPLING 327 8.3 NUMERICAL SUMMARIES 332 8.3.1 SAMPLE MEAN 333 8.3.2
SAMPLE MEDIAN 334 8.3.3 SAMPLE VARIANCE 334 8.3.4 MEDIAN ABSOLUTE
DEVIATION 335 8.3.5 PERCENTILE-BASED MEASURES OF DISPERSION 335 8.3.6
SAMPLE SKEWNESS 337 8.3.7 SAMPLE KURTOSIS 338 8.3.8 AN EXAMPLE 338 X
TABLE OF CONTENTS 8.4 GRAPHICAL SUMMARIES 341 8.4.1 QUANTILE-QUANTILE
PLOTS 342 8.4.2 HISTOGRAMS 345 8.4.3 STEM-AND-LEAF PLOTS 346 CHAPTER
SUMMARY 349 REVIEW EXERCISES 350 CHAPTER 9 SAMPLING DISTRIBUTIONS 9.1
INTRODUCTION 351 9.2 DISTRIBUTIONS BASED ON SAMPLES FROM NORMAL
POPULATIONS 9.3 INDEPENDENCE OF X AND S 2 359 9.4 ORDER STATISTICS 362
CHAPTER SUMMARY 377 REVIEW EXERCISES 378 CHAPTER 10 POINT ESTIMATION
10.1 INTRODUCTION 381 10.2 MAXIMUM LIKELIHOOD ESTIMATION 382 10.3 METHOD
OF MOMENTS 390 10.4 PROPERTIES OF ESTIMATORS 394 10.4.1 UNBIASEDNESS 394
10.4.2 EFFICIENCY 398 10.4.3 SUFFLCIENCY 408 10.4.4 MINIMAL SUFFICIENT
STATISTICS 417 10.4.5 COMPLETENESS 419 10.5 LARGE SAMPLE PROPERTIES OF
ESTIMATORS 430 10.5.1 CONSISTENCY 430 10.5.2 ASYMPTOTIC EFFICIENCY 432
10.6 BAYES ESTIMATORS 434 10.7 ROBUST ESTIMATION 441 CHAPTER SUMMARY 444
REVIEW EXERCISES 449 TABLE OF CONTENTS XI CHAPTER 11 CONFIDENCE
INTERVALS 451 11.1 INTRODUCTION 451 11.2 PIVOTAL QUANTITY METHOD 453
11.3 METHOD BASED ON SAMPLING DISTRIBUTIONS 463 11.4 LARGE SAMPLE
CONFIDENCE INTERVALS 468 11.5 A NONPARAMETNC CONFIDENCE INTERVAL 472
CHAPTER SUMMARY 474 REVIEW EXERCISES 476 CHAPTER 12 HYPOTHESIS TESTING
479 12.1 INTRODUCTION 479 12.2 TYPES OF ERRORS 481 12.3 TESTING SIMPLE
HYPOTHESES 489 12.4 UNIFORMLY MOST POWERFUL TESTS 497 12.5 LIKELIHOOD
RATIO TESTS 509 12.6 CHI-SQUARE TESTS 528 12.7 LARGE SAMPLE TESTS 535
12.8 SEQUENTIAL PROBABILITY RATIO TEST 540 12.9 NONPARAMETRIC TESTS 546
12.9.1 SIGN TEST 547 12.9.2 WILCOXON SIGNED RANK TEST 551 12.9.3
WILCOXON RANK SUM TEST 553 CHAPTER SUMMARY 558 REVIEW EXERCISES 564
CHAPTER 13 REGRESSION AND CORRELATION 569 13.1 INTRODUCTION 569 13.2
SIMPLE LINEAR REGRESSION 570 13.3 MATRIX CALCULUS 589 13.4 MULTIPLE
REGRESSION 595 13.5 CORRELATION 607 13.6 NONPARAMETRIC METHODS 615
CHAPTER SUMMARY 622 REVIEW EXERCISES 630 XII TABLE OF CONTENTS - CHAPTER
14 ANALYSIS OF VARIANCE 14.1 INTRODUCTION 633 14.2 EXPERIMENTAL DESIGN
634 14.3 ONE-WAY ANALYSIS OF VARIANCE 14.4 TWO-WAY ANALYSIS OF VARIANCE
14.5 ESTIMATION 667 14.6 NONPARAMETRIC METHODS 673 CHAPTER SUMMARY 681
REVIEW EXERCISES 687 633 641 652 APPENDIX A STATISTICAL TABLES
I*BINOMIAL DISTRIBUTION A.L II*POISSON DISTRIBUTION A.7 III*NORMAL
DISTRIBUTION A.L3 IV*CHI-SQUARE DISTRIBUTION A.14 V*STUDENT S T
DISTRIBUTION A.L 5 VI* F DISTRIBUTION A.L6 VII*WILCOXON SIGNED RANK TEST
A.20 VIII*WILCOXON RANK SUM TEST A.27 IX*SPEARMAN S RHO A.35
X*KRUSKAL-WALLIS TEST A.38 XI*FRIEDMAN TEST A.53 APPENDIX B PROBABILITY
DISTRIBUTIONS DISCRETE RANDOM VARIABLES A.59 CONTINUOUS RANDOM VARIABLES
A.61 A.1 A.59 APPENDIX C BIBLIOGRAPHY APPENDIX D ANSWERS TO SELECTED
ODD-NUMBERED EXERCISES INDEX A.63 A.65 LI J RANDOM EXPERIMENTS AND
PROBABILITY MOST PEOPLE KNOW INTUITIVELY WHAT THE WORD PROBABILITY
MEANS. MANY OF US HAVE ENCOUNTERED PROBABILITIES IN OUR DAILY
ACTIVITIES. FOR EXAMPLE, IF WE FLIP A COIN IT IS OUR UNDERSTANDING THAT
HEADS SHOULD RESULT ABOUT HALF THE TIME. WHEN A LOCAL WEATHER FORECASTER
STATES THAT THERE IS A 40 PERCENT CHANCE FOR RAIN TOMORROW WE HAVE A
GENERAL UNDERSTANDING THAT WHAT IS MEANT IS THAT, GIVEN THE CURRENT
CONDITIONS, RAIN MAY OCCUR 4 TIMES OUT OF 10. IF WE PLAY BRIDGE, WE MAY
DRAW ON PAST EXPERIENCE TO ASSESS THE LIKELIHOOD THAT THE CARDS HELD BY
OUR OPPONENTS HAVE BEEN DISTRIBUTED IN A CERTAIN WAY IN ORDER TO PLAN
HOW WE PLAY A CURRENT HAND. IN FACT, ANYONE WHO IS CONSISTENTLY
SUCCESSFUL AT GAMES INVOLVING CHANCE SUCH AS POKER AND BACKGAMMON IS
WELL AWARE OF THE RELATIVE FREQUENCY OF THE VARIOUS POSSIBLE OUTCOMES IN
THE PLAY OF THE GAME. THE SITUATIONS MENTIONED ABOVE HAVE SOME THINGS IN
COMMON. IN EACH WE FACE A SITUATION THAT IS, AT LEAST IN PRINCIPLE, WELL
DEFINED AND REPEATABLE. THE POSSIBLE OUTCOMES ARE KNOWN, BUT THE
PARTICULAR OUTCOME THAT WILL TAKE PLACE THIS TIME CANNOT BE PREDICTED.
WHAT PROBABILITY ATTEMPTS TO DO IS TO DETERMINE A NUMERICAL VALUE THAT
TEILS WHAT PROPORTION OF THE TIME EACH POSSIBILITY WILL OCCUR. ONE COULD
CORRECTLY ARGUE THAT THE WEATHER EXAMPLE IS NOT LIKE THE OTHERS. IT DOES
NOT INVOLVE CHANCE OCCURRENCES BUT RATHER REPRESENTS A LESS THAN
COMPLETE UNDERSTANDING OF THE PHYSICS OF THE ATMOSPHERE. THIS IS THE
CASE IN A NUMBER OF AREAS WHERE PROBABILITY MAY BE APPLIED. MANY
PHYSICAL SITUATIONS ARE SO COMPLI- CATED THAT IT IS NOT FEASIBLE TO
DEVELOP A MATHEMATICAL MODEL THAT ACCOUNTS FOR ALL OF THE VARIABLES. IN
SUCH CASES IT IS COMMON TO DEVELOP MODEIS THAT USE THE MAIN VARIABLES
AND THEN LUMP TOGETHER THE UNUSED VARIABLES IN A TERM THAT REPRESENTS
THE UNPREDICTED PART OF THE MODEL CALLED THE NOISE. THE NOISE IN THE
MODEL IS WHAT INJECTS RANDOMNESS INTO PREDICTIONS.
|
| any_adam_object | 1 |
| author | Rinaman, William C. |
| author_facet | Rinaman, William C. |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 0030718066 |
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| spelling | Rinaman, William C. Verfasser aut Foundations of probability and statistics William C. Rinaman Forth Worth u.a. Saunders College Publ. 1993 Getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Estatística (textos elementares) larpcal Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Statistik (DE-588)4056995-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006384817&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rinaman, William C. Foundations of probability and statistics Estatística (textos elementares) larpcal Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4079013-7 |
| title | Foundations of probability and statistics |
| title_auth | Foundations of probability and statistics |
| title_exact_search | Foundations of probability and statistics |
| title_full | Foundations of probability and statistics William C. Rinaman |
| title_fullStr | Foundations of probability and statistics William C. Rinaman |
| title_full_unstemmed | Foundations of probability and statistics William C. Rinaman |
| title_short | Foundations of probability and statistics |
| title_sort | foundations of probability and statistics |
| topic | Estatística (textos elementares) larpcal Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Estatística (textos elementares) Mathematical statistics Probabilities Statistik Wahrscheinlichkeitstheorie |
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