Normal view MARC view

An Introduction to probability theory and its applications

Author: Feller, William Series: Wiley series in probability and mathematical statistics Publisher: Wiley, 1968.Edition: 3rd ed.Language: EnglishDescription: 509 p. ; 24 cm.ISBN: 0471257087Type of document: BookNote: Doriot and Tanoto: for 2016-2017 coursesBibliography/Index: Includes index List(s) this item appears in: Textbooks for Discrete Stochastic Processes / Stephen Chick / PhD 2016-2017 | Textbooks for Probability and Statistics A / Spyros Zoumpoulis / PhD 2016-2017
Tags: No tags from this library for this title. Add tag(s)
Log in to add tags.
Item type Current location Collection Call number Status Date due
Book Doriot Library
Main Collection
Print QA273 .F45 1968 Vol.1
(Browse shelf)
001352855
Available
Book Doriot Library
Main Collection
Print QA273 .F45 1968 Vol.1
(Browse shelf)
000127252
Available
Book Tanoto Library
Textbook Collection (PhD)
Print QA273 .F45 1968 Vol.1
(Browse shelf)
900216176
Consultation only
Book Tanoto Library
Textbook Collection (PhD)
Print QA273 .F45 1968 Vol.1
(Browse shelf)
900045471
Available

Doriot and Tanoto: for 2016-2017 courses

Includes index

Digitized

Contents CHAPTER INTRODUCTION: THE NATURE OF PAGE PROBABILITY THEORY . 1. 2. 3. 4. 5. The Background . . . Procedure . . . . . . "Statistical" Probability Summary . . . . . . Historical Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 3 4 5 6 7 7 9 13 14 17 19 22 24 26 26 28 31 34 38 40 42 43 47 50 52 54 54 I THE SAMPLE SPACE. . . . . . . . . . . . . . . . . 1. The Empirical Background . . . . . . . . . . . . 2. Examples . . . . . . . . . . . . . . . . . . . 3. The Sample Space. Events . . . . . . . . . . . . 4. Relations among Events . . . . . . . . . . . . . 5. Discrete Sample Spaces . . . . . . . . . . . . . 6. Probabilities in Discrete Sample Spaces : Preparations 7. The Basic Definitions and Rules . . . . . . . . . 8. Problems for Solution . . . . . . . . . . . . . . II ELEMENTS 1. Preliminaries . . . . . . . . . . . . . . . . . . 2. Ordered Samples . . . . . . . . . . . . . . . . 3. Examples . . . . . . . . . . . . . . . . . . . 4. Subpopulations and Partitions . . . . . . . . . . *5. Application to Occupancy Problems . . . . . . . . *5a. Bose-Einstein and Fermi-Dirac Statistics . . . . . . *5b. Application to Runs . . . . . . . . . . . . . . . 6. The Hypergeometric Distribution . . . . . . . . . 7. Examples for Waiting Times . . . . . . . . . . . 8. Binomial Coefficients . . . . . . . . . . . . . . 9. Stirling's Formula . . . . . . . . . . . . . . . . Problems for Solution: . . . . . . . . . . . . . . . 10. Exercises and Examples . . . . . . . . . . . . . OF COMBINATORIAL ANALYSIS. . . . . . . . * Starred sections are not required for the understanding of the sequel and should be omitted at first reading. xiii ... xiv CHAPTER CONTENTS PAGE CHAPTER CONTENTS xv PAGE 11. Problems and Complements of a Theoretical Character . . . . . . . . . . . . . . . . . . 12. Problems and Identities Involving Binomial Coefficients . . . . . . . . . . . . . . . . . . *III FLUCTUATIONS IN COIN TOSSING AND RANDOM WALKS 1. General Orientation. The Reflection Principle . . 2. Random Walks: Basic Notions and Notations . . 3. The Main Lemma. . . . . . . . . . . . . . . 4. Last Visits and Long Leads. . . . . . . . . . . *5. Changes of Sign . . . . . . . . . . . . . . . 6. An Experimental Illustration . . . . . . . . . . 7. Maxima and First Passages. . . . . . . . . . . 8. Duality. Position of Maxima . . . . . . . . . . 9. An Equidistribution Theorem. . . . . . . . . . 10. Problems for Solution . . . . . . . . . . . . . *IV COMBINATION OF EVENTS . . . . . . . . 1. Union of Events . . . . . . . . . . 2. Application to the Classical Occupancy 3. The Realization of m among N events . 4. Application to Matching and Guessing. 5. Miscellany . . . . . . . . . . . . . 6. Problems for Solution . . . . . . . . . 58 63 67 68 73 76 78 84 86 88 91 94 95 98 98 101 106 107 109 111 114 114 118 125 128 132 136 139 140 146 146 147 150 152 . . . . . . . . . . 5. 6. 7. 8. 9. 10. The Poisson Approximation . . . . . . . . . . . The Poisson Distribution. . . . . . . . . . . . . Observations Fitting the Poisson Distribution. . . . Waiting Times. The Negative Binomial Distribution The Multinomial Distribution. . . . . . . . . . . Problems for Solution . . . . . . . . . . . . . . 153 156 159 164 167 169 174 174 179 182 187 190 192 193 196 196 198 200 202 204 208 210 212 212 220 223 227 229 233 234 236 237 243 243 246 248 VII THE NORMAL APPROXIMATION 1. 2. 3. 4. 5. *6. 7. TO THE BINOMIAL DISTRIBUTION. . . . . . . . . . . . . . . . . . . . The Normal Distribution. . . . . . . . . . . . . Orientation: Symmetric Distributions . . . . . . . The DeMoivre-Laplace Limit Theorem. . . . . . . Examples . . . . . . . . . . . . . . . . . . . Relation to the Poisson Approximation . . . . . . Large Deviations . . . . . . . . . . . . . . . . Problems for Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem . . . . . . . . . . . . . . . . . . . . . . . . . . V CONDITIONAL PROBABILITY. STOCHASTIC INDEPENDENCE . 1. Conditional Probability . . . . . . . . . . . . . 2. Probabilities Defined by Conditional Probabilities. Urn Models . . . . . . . . . . . . . . . . . . 3. Stochastic Independence . . . . . . . . . . . . . 4. Product Spaces. Independent Trials . . . . . . . . *5. Applications to Genetics . . . . . . . . . . . . . *6. Sex-Linked Characters . . . . . . . . . . . . . . *7. Selection . . . . . . . . . . . . . . . . . . . . 8. Problems for Solution . . . . . . . . . . . . . . VI THE BINOMIAL AND THE POISSON DISTRIBUTIONS . . . 1. Bernoulli Trials . . . . . . . . . . . . . . . . 2. The Binomial Distribution . . . . . . . . . . . 3. The Central Term and the Tails . . . . . . . . . 4. The Law of Large Numbers . . . . . . . . . . . *VIII UNLIMITED SEQUENCES OF BERNOULLI TRIALS . 1. Infinite Sequences of Trials . . . . . . . . 2. Systems of Gambling . . . . . . . . . . 3. The Borel-Cantelli Lemmas. . . . . . . . 4. The Strong Law of Large Numbers . . . . 5. The Law of the Iterated Logarithm . . . . 6. Interpretation in Number Theory Language 7. Problems for Solution . . . . . . . . . . IX RANDOM VARIABLES; EXPECTATION . 1. Random Variables . . . . . . 2. Expectations . . . . . . . . . 3. Examples and Applications . . . 4. The Variance . . . . . . . . . 5. Covariance; Variance of a Sum. 6. Chebyshev's Inequality. . . . . *7. Kolmogorov's Inequality. . . . *8. The Correlation Coefficient . . . 9. Problems for Solution . . . . . X LAWS OF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LARGE NUMBERS. . . . . . . . . . . . . . 1. Identically Distributed Variables . . . . . . . . . *2. Proof of the Law of Large Numbers . . . . . . . . 3. The Theory of "Fair" Games. . . . . . . . . . . xvi CHAPTER CONTENTS PAGE CHAPTER CONTENTS xvii PAGE *4. 5. *6. *7. 8. 1. 2. 3. 4. 5. *6. 7. The Petersburg Game . . . . . . . . Variable Distributions . . . . . . . . Applications to Combinatorial Analysis The Strong Law of Large Numbers . . Problems for Solution . . . . . . . . Generalities . . . . . . . . . Convolutions . . . . . . . . . Equalizations and Waiting Times Partial Fraction Expansions . . Bivariate Generating Functions . The Continuity Theorem . . . . Problems for Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 253 256 258 261 264 264 266 270 275 279 280 283 286 286 288 292 293 295 298 301 303 303 307 311 313 316 320 322 326 328 329 335 338 342 342 344 3. *4. *5. 6. *7. 8. 9. XI INTEGRAL VALUED VARIABLES. GENERATING FUNCTIONS . . . . . . . . . . . . . in Bernoulli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trials . . . . . . . . . . . . . . . . . . . . . . . . . . Expected Duration of the Game . . . . . . . . . Generating Functions for the Duration of the Game and for the First-Passage Times. . . . . . . . . . Explicit Expressions . . . . . . . . . . . . . . . Connection with Diffusion Processes. . . . . . . . Random Walks in the Plane and Space . . . . . . The Generalized One-Dimensional Random Walk (Sequential Sampling) . . . . . . . . . . . . . . Problems for Solution . . . . . . . . . . . . . . 348 349 352 354 359 363 367 372 372 375 382 384 387 390 392 399 404 406 407 414 419 424 428 428 432 436 438 443 444 444 446 448 451 454 458 XV MARKOV CHAINS . . . . . . . . . . . . . . . . . . *XII COMPOUND DISTRIBUTIONS. BRANCHING PROCESSES . . . 1. Sums of a Random Number of Variables. . . . 2. The Compound Poisson Distribution . . . . . 2a. Processes with Independent Increments . . . . 3. Examples for Branching Processes. . . . . . . 4. Extinction Probabilities in Branching Processes . 5. The Total Progeny in Branching Processes . . . 6. Problems for Solution . . . . . . . . . . . . XIII RECURRENT EVENTS. RENEWAL THEORY 1. 2. 3. 4. 5. *7. *8. 9. 10. *11. 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A General Limit Theorem . . . . . . . . . Application to the Theory of Success Runs . . . . . More General Patterns. . . . . . . . . . . . . . Lack of Memory of Geometric Waiting Times . . . Renewal Theory . . . . . . . . . . . . . . . . Proof of the Basic Limit Theorem . . . . . . . . . Problems for Solution . . . . . . . . . . . . . . AND Informal Preparations and Definitions . . . . . . . The Basic Relations . . . Examples . . . . . . . Delayed Recurrent Events. Examples . . . . . . . 1. Definition . . . . . . . . . . . . . . . 2. Illustrative Examples . . . . . . . . . . 3. Higher Transition Probabilities . . . . . . 4. Closures and Closed Sets. . . . . . . . . 5. Classification of States . . . . . . . . . . 6. Irreducible Chains. Decompositions . . . . 7. Invariant Distributions. . . . . . . . . . 8. Transient Chains . . . . . . . . . . . . 9. Periodic Chains . . . . . . . . . . . . . 10. Application to Card Shuffling. . . . . . . *1l. Invariant Measures. Ratio Limit Theorems * 12. Reversed Chains. Boundaries . . . . . . 13. The General Markov Process . . . . . . . 14. Problems for Solution . . . . . . . . . . *XVI ALGEBRAIC TREATMENT OF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FINITE MARKOV CHAINS . . 1. 2. 3. 4. 5. General Theory . . . . . . . . . . . . . . Examples . . . . . . . . . . . . . . . . Random Walk with Reflecting Barriers . . . Transient States; Absorption Probabilities . . Application to Recurrence Times . . . . . . . . . . . . . . . . . . . . . XVII THE SIMPLEST TIME-DEPENDENT STOCHASTIC PROCESSES . XIV RANDOM WALK 1. General Orientation . . . . . . . . . . . . . . . 2. The Classical Ruin Problem . . . . . . . . . . . RUIN PROBLEMS. . . . . . . . . 1. 2. 3. *4. 5. 6. General Orientation. Markov Processes The Poisson Process . . . . . . . . . The Pure Birth Process. . . . . . . . Divergent Birth Processes . . . . . . The Birth and Death Process . . . . . Exponential Holding Times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. CHAPTER CONTENTS PAGE 7. 8. 9. 10. ANSWERS Waiting Line and Servicing Problems . . . . . The Backward (Retrospective) Equations . . . . General Processes . . . . . . . . . . . . . . Problems for Solution . . . . . . . . . . . . TO . . . . . . . . 460 468 470 478 483 499 PROBLEMS. . . . . . . . . . . . . . . . . . . INDEX . . . . . . . . . . . . . . . . . . . . . . . . . .

There are no comments for this item.

Log in to your account to post a comment.
Koha 3.18 - INSEAD Library Catalogue
Library Home | Contact Us | What's Koha?