A first course in probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Pearson Prentice Hall
2010
|
| Edition: | 8. ed., internat. ed. |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018605126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 530 S. graph. Darst. |
| ISBN: | 0136079091 9780136079095 |
Staff View
MARC
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| 100 | 1 | |a Ross, Sheldon M. |d 1943- |e Verfasser |0 (DE-588)123762235 |4 aut | |
| 245 | 1 | 0 | |a A first course in probability |c Sheldon Ross |
| 250 | |a 8. ed., internat. ed. | ||
| 264 | 1 | |a Upper Saddle River, NJ |b Pearson Prentice Hall |c 2010 | |
| 300 | |a XIII, 530 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Probabilidade (textos elementares) |2 larpcal | |
| 650 | 4 | |a Probabilities |v Textbooks | |
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Record in the Search Index
| DE-BY-TUM_call_number | 0002 MAT 600 2009 B 3043(8) 0004 MAT 600 2009 B 3043(8) 0102 DAT 600 2005 A 7509(8) |
|---|---|
| DE-BY-TUM_katkey | 1707969 |
| DE-BY-TUM_location | 00 01 |
| DE-BY-TUM_media_number | 040006975586 040006975575 040071470209 |
| _version_ | 1832569019680423936 |
| adam_text | Contents
Preface
xi
1
Combinatorial Analysis
1
1.1
Introduction
................................. 1
1.2
The Basic Principle of Counting
...................... 1
1.3
Permutations
................................. 3
1.4
Combinations
................................ 5
1.5
Multinomial Coefficients
.......................... 9
1.6
The Number of Integer Solutions of Equations
............. 12
Summary
................................... 15
Problems
................................... 16
Theoretical Exercises
............................ 18
Self-Test Problems and Exercises
..................... 20
2
Axioms of Probability
22
2.1
Introduction
................................. 22
2.2
Sample Space and Events
.......................... 22
2.3
Axioms of Probability
............................ 26
2.4
Some Simple Propositions
......................... 29
2.5
Sample Spaces Having Equally Likely Outcomes
............ 33
2.6
Probability as a Continuous Set Function
................. 44
2.7
Probability as a Measure of Belief
..................... 48
Summary
................................... 49
Problems
................................... 50
Theoretical Exercises
............................ 54
Self-Test Problems and Exercises
..................... 56
3
Conditional Probability and Independence
58
3.1
Introduction
................................. 58
3.2
Conditional Probabilities
.......................... 58
3.3
Bayes s Formula
............................... 65
3.4
Independent Events
............................. 79
3.5
P(-|F) Is a Probability
............................ 93
Summary
................................... 101
Problems
................................... 102
Theoretical Exercises
............................ 110
Self-Test Problems and Exercises
..................... 114
4
Random Variables
117
4.1
Random Variables
.............................. 117
4.2
Discrete Random Variables
........................ 123
4.3
Expected Value
............................... 125
4.4
Expectation of a Function of a Random Variable
............ 128
4.5
Variance
................................... 132
4.6
The Bernoulli and Binomial Random Variables
............. 134
4.6.1
Properties of Binomial Random Variables
............ 139
4.6.2
Computing the Binomial Distribution Function
......... 142
vii
viii Contents
4.7
The
Poisson
Random Variable
....................... 143
4.7.1
Computing the
Poisson
Distribution Function
.......... 154
4.8
Other Discrete Probability Distributions
................. 155
4.8.1
The Geometric Random Variable
................. 155
4.8.2
The Negative Binomial Random Variable
............ 157
4.8.3
The Hypergeometric Random Variable
............. 160
4.8.4
The
Zeta
(or Zipf) Distribution
.................. 163
4.9
Expected Value of Sums of Random Variables
............. 164
4.10
Properties of the Cumulative Distribution Function
........... 168
Summary
................................... 170
Problems
................................... 172
Theoretical Exercises
............................ 179
Self-Test Problems and Exercises
..................... 183
Continuous Random Variables
186
5.1
Introduction
................................. 186
5.2
Expectation and Variance of Continuous Random Variables
..... 190
5.3
The Uniform Random Variable
...................... 194
5.4
Normal Random Variables
......................... 198
5.4.1
The Normal Approximation to the Binomial Distribution
. . . 204
5.5
Exponential Random Variables
...................... 208
5.5.1
Hazard Rate Functions
....................... 212
5.6
Other Continuous Distributions
...................... 215
5.6.1
The Gamma Distribution
..................... 215
5.6.2
The Weibull Distribution
..................... 216
5.6.3
The Cauchy Distribution
...................... 217
5.6.4
The Beta Distribution
....................... 218
5.7
The Distribution of a Function of a Random Variable
......... 219
Summary
................................... 222
Problems
................................... 224
Theoretical Exercises
............................ 227
Self-Test Problems and Exercises
..................... 229
Jointly Distributed Random Variables
232
6.1
Joint Distribution Functions
........................ 232
6.2
Independent Random Variables
...................... 240
6.3
Sums of Independent Random Variables
................. 252
6.3.1
Identically Distributed Uniform Random Variables
...... 252
6.3.2
Gamma Random Variables
.................... 254
6.3.3
Normal Random Variables
.................... 256
6.3.4
Poisson
and Binomial Random Variables
............ 259
6.3.5
Geometric Random Variables
................... 260
6.4
Conditional Distributions: Discrete Case
................. 263
6.5
Conditional Distributions: Continuous Case
............... 266
6.6
Order Statistics
............................... 270
6.7
Joint Probability Distribution of Functions of Random Variables
. . . 274
6.8
Exchangeable Random Variables
..................... 282
Summary
................................... 285
Problems
................................... 287
Theoretical Exercises
............................ 291
Self-Test Problems and Exercises
..................... 293
Contents ix
Properties of Expectation
297
7.1
Introduction
................................. 297
7.2
Expectation of Sums of Random Variables
................ 298
7.2.1
Obtaining Bounds from Expectations
via the Probabilistic Method
.................... 311
7.2.2
The
Maximum-Minimums
Identity
................ 313
7.3
Moments of the Number of Events that Occur
.............. 315
7.4
Covariance, Variance of Sums, and Correlations
............. 322
7.5
Conditional Expectation
.......................... 331
7.5.1
Definitions
.............................. 331
7.5.2
Computing Expectations by Conditioning
............ 333
7.5.3
Computing Probabilities by Conditioning
............ 344
7.5.4
Conditional Variance
........................ 347
7.6
Conditional Expectation and Prediction
................. 349
7.7
Moment Generating Functions
....................... 354
7.7.1
Joint Moment Generating Functions
............... 363
7.8
Additional Properties of Normal Random Variables
.......... 365
7.8.1
The Multivariate Normal Distribution
.............. 365
7.8.2
The Joint Distribution of the Sample Mean
and Sample Variance
........................ 367
7.9
General Definition of Expectation
..................... 369
Summary
................................... 370
Problems
................................... 373
Theoretical Exercises
............................ 380
Self-Test Problems and Exercises
..................... 384
Limit Theorems
388
8.1
Introduction
................................. 388
8.2
Chebyshev^s Inequality and the Weak Law of Large
Numbers
....... ............................ 388
8.3
The Central Limit Theorem
........................ 391
8.4
The Strong Law of Large Numbers
.................... 400
8.5
Other Inequalities
.............................. 403
8.6
Bounding the Error Probability When Approximating a Sum of
Independent Bernoulli Random Variables by
a Poisson
Random Variable
.............................. 410
Summary
................................... 412
Problems
................................... 412
Theoretical Exercises
............................ 414
Self-Test Problems and Exercises
..................... 415
Additional Topics in Probability
417
9.1
The
Poisson
Process
............................. 417
9.2
Markov Chains
................................ 419
9.3
Surprise. Uncertainty, and Entropy
.................... 425
9.4
Coding Theory and Entropy
........................ 428
Summary
................................... 434
Problems and Theoretical Exercises
.................... 435
Self-Test Problems and Exercises
..................... 436
References
.................................. 436
χ
Contents
10 Simulation 438
10.1
Introduction
................................. 438
10.2 General
Techniques
for Simulating Continuous Random Variables
. . 440
10.2.1
The Inverse Transformation Method
............... 441
10.2.2
The Rejection Method
....................... 442
10.3
Simulating from Discrete Distributions
.................. 447
10.4
Variance Reduction Techniques
...................... 449
10.4.1
Use of Antithetic Variables
.................... 450
10.4.2
Variance Reduction by Conditioning
............... 451
10.4.3
Control
Variâtes
.......................... 452
Summary
................................... 453
Problems
................................... 453
Self-Test Problems and Exercises
..................... 455
Reference
.................................. 455
Answers to Selected Problems
457
Solutions to Self-Test Problems and Exercises
461
Index
521
|
| any_adam_object | 1 |
| author | Ross, Sheldon M. 1943- |
| author_GND | (DE-588)123762235 |
| author_facet | Ross, Sheldon M. 1943- |
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| classification_rvk | SK 800 ST 600 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)237199460 (DE-599)BSZ286052210 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 8. ed., internat. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035744981 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:59:12Z |
| institution | BVB |
| isbn | 0136079091 9780136079095 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018605126 |
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| owner_facet | DE-91 DE-BY-TUM DE-11 DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | XIII, 530 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Pearson Prentice Hall |
| record_format | marc |
| spellingShingle | Ross, Sheldon M. 1943- A first course in probability Probabilidade (textos elementares) larpcal Probabilities Textbooks Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | A first course in probability |
| title_auth | A first course in probability |
| title_exact_search | A first course in probability |
| title_full | A first course in probability Sheldon Ross |
| title_fullStr | A first course in probability Sheldon Ross |
| title_full_unstemmed | A first course in probability Sheldon Ross |
| title_short | A first course in probability |
| title_sort | a first course in probability |
| topic | Probabilidade (textos elementares) larpcal Probabilities Textbooks Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Probabilidade (textos elementares) Probabilities Textbooks Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018605126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosssheldonm afirstcourseinprobability |
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