Introduction to probability models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego [u.a.]
Acad. Press
2000
|
| Edition: | 7. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 693 S. graph. Darst. |
| ISBN: | 0125984758 |
Staff View
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| 245 | 1 | 0 | |a Introduction to probability models |c Sheldon M. Ross |
| 250 | |a 7. ed. | ||
| 264 | 1 | |a San Diego [u.a.] |b Acad. Press |c 2000 | |
| 300 | |a XV, 693 S. |b graph. Darst. | ||
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| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Probabilités - Problèmes et exercices | |
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Record in the Search Index
| _version_ | 1804127771182497792 |
|---|---|
| adam_text | Contents
Preface to the Fifth Edition
xl
Preface to the Sixth Edition
xiii
Preface to the Seventh Edition
xv
ì
ra
rrooaDiiity
ι
neory
1.1.
Introduction
1
1.2.
Sample Space and Events
1
1.3.
Probabilities Defined on Events
4
1.4.
Conditional Probabilities
6
1.5.
Independent Events
10
1.6.
Bayes
Formula
12
Exercises
15
References
21
2.
Random Variables
23
2.1.
Random Variables
23
2.2.
Discrete Random Variables
27
2.2.1.
The Bernoulli Random Variable
27
2.2.2.
The Binomial Random Variable
28
2.2.3.
The Geometric Random Variable
31
2.2.4.
The
Poisson
Random Variable
31
2.3.
Continuous Random Variables
33
2.3.1.
The Uniform Random Variable
34
2.3.2.
Exponential Random Variables
35
2.3.3.
Gamma Random Variables
35
2.3.4.
Normal Random Variables
36
2.4.
Expectation of a Random Variable
37
2.4.1.
The Discrete Case
37
2.4.2.
The Continuous Case
40
2.4.3.
Expectation of a Function of a Random Variable
42
2.5.
Jointly Distributed Random Variables
46
2.5.1.
Joint Distribution Functions
46
2.5.2.
Independent Random Variables
50
2.5.3.
Covariance and Variance of Sums of Random Variables
51
2.5.4.
Joint Probability Distribution of Functions of Random
Variables
59
2.6.
Moment Generating Functions
62
2.6.1.
The Joint Distribution of the Sample Mean and Sample
Variance from a Normal Population
70
2.7.
Limit Theorems
73
2.8.
Stochastic Processes
79
Exercises
82
References
92
B. Conditional Probability and Conditional
Expectation
93
3.1.
Introduction
93
3.2.
The Discrete Case
93
3.3.
The Continuous Case
98
3.4.
Computing Expectations by Conditioning
101
3.5.
Computing Probabilities by Conditioning
114
3.6.
Some Applications
128
3.6.1.
A List Model
128
3.6.2.
A Random Graph
129
3.6.3.
Uniform Priors, Polya s Urn Model, and
Bose-Einstein Statistics
137
3.6.4.
The k-Record Values of Discrete Random Variables
141
Exercises
145
4.
Markov Chains
163
4.1.
Introduction
163
4.2.
Chapman-Kohnogorov Equations
166
4.3.
Classification of States
168
4.4.
Limiting Probabilities
178
4.5.
Some Applications
188
4.5.1.
The Gamblers Ruin Problem
188
4.5.2.
A Model for Algorithmic Efficiency
192
4.5.3.
Using a Random Walk to Analyze a Probabilistic
Algorithm for the Satisfiability Problem
194
4.6.
Mean Time Spent in Transient States
200
4.7.
Branching Processes
202
4.8.
Time Reversible Markov Chains
205
4.9.
Markov Chain Monte Carlo Methods
216
4.10.
Markov Decision Processes
222
Exercises
226
References
240
5,
The Exponential Distribution and the
Poisson
Process
24Ί
5.1.
Introduction
241
5.2.
The Exponential Distribution
242
5.2.1.
Definition
242
5.2.2.
Properties of the Exponential Distribution
243
5.2.3.
Further Properties of the Exponential Distribution
248
5.2.4.
Convolutions of Exponential Random Variables
253
5.3.
The
Poisson
Process
256
5.3.1.
Counting Processes
256
5.3.2.
Definition of the
Poisson
Process
258
5.3.3.
Interarrival and Waiting Time Distributions
261
5.3.4.
Further Properties of
Poisson
Processes
264
5.3.5.
Conditional Distribution of the Arrival Times
270
5.3.6.
Estimating Software Reliability
281
5.4.
Generalizations of the
Poisson
Process
284
5.4.1.
Nonhomogeneous
Poisson
Process
284
5.4.2.
Compound
Poisson
Process
289
Exercises
295
References
311
őo
Continuous-Time Markov
Chalos
313
6.
L
Introduction
313
6.2.
Continuous-Time Markov Chains
314
6.3.
Birth and Death Processes
316
6.4.
The Transition Probability Function
Р^{і)
323
6.5.
Limiting Probabilities
331
6.6.
Time Reversibility
338
6.7.
Uniformization
346
6.8.
Computing the Transition Probabilities
349
Exercises
352
References
361
7.
Renewal Theory and Its Applications
363
7.1.
Introduction
363
7.2.
Distribution of N(t)
365
7.3.
Limit Theorems and Their Applications
368
7.4.
Renewal Reward Processes
377
7.5.
Regenerative Processes
386
7.5.1.
Alternating Renewal Processes
389
7.6.
Semi-Markov Processes
395
7.7.
The Inspection Paradox
398
7.8.
Computing the Renewal Function
400
7.9.
Applications to Patterns
403
7.9.1.
Patterns of Discrete Random Variables
404
7.9.2.
The Expected Time to a Maximal Run of Distinct
Values
410
7.9.3.
Increasing Runs of Continuous Random Variables
412
Exercises
413
References
425
8.
Queueing Theory
427
8.1.
Introduction
427
8.2.
Preliminaries
428
8.2
Л
.
Cost Equations
429
8.2.2.
Steady-State Probabilities
430
8.3.
Exponential Models
432
8.3.1.
A Single-Server Exponential Queueing System
432
8.3.2.
A Single-Server Exponential Queueing System
Having Finite Capacity
438
8.3.3.
A Shoeshine Shop
442
8.3.4.
A Queueing System with Bulk Service
444
8.4.
Network of Queues
447
8.4.1.
Open Systems
447
8.4.2.
Closed Systems
452
8.5.
The System M/G/l
458
8.5.1.
Preliminaries: Work and Another Cost Identity
458
8.5.2.
Application of Work to M/G/l
459
8.5.3.
Busy Periods
460
8.6.
Variations on the M/G/l
461
8.6.1.
The M/G/l with Random-Sized Batch Arrivals
461
8.6.2.
Priority Queues
463
8.63.
An
M/G/Ì
Optimization Example
466
8.7.
The Model
G/M/Ì
470
8.7.1.
The G/M/l Busy and Idle Periods
475
8.8.
A Finite Source Model
475
8.9.
Multiserver Queues
479
8.9.1.
Erlang s Loss System
479
8.9.2.
The
M/M
/k Queue
481
8.9.3.
The G/M/k Queue
481
8.9.4.
The M/G/k Queue
483
Exercises
484
References
496
9»
Reliability Theory
499
9.1.
Introduction
499
9.2.
Structure Functions
500
9.2.1.
Minimal Path and Minimal Cut Sets
502
9.3.
Reliability of Systems of Independent Components
506
9.4.
Bounds on the Reliability Function
510
9.4.1.
Method of Inclusion and Exclusion
511
9.4.2.
Second Method for Obtaining Bounds on r(p)
519
9.5.
System Life as a Function of Component Lives
521
9.6.
Expected System Lifetime
529
9.6.1.
An Upper Bound on the Expected Life of a
Parallel System
533
9.7.
Systems with Repair
535
9.7.1.
A Series Model with Suspended Animation
539
Exercises
542
References
548
10.
Brownian Motion and Stationary Processes
549
10.1.
Brownian Motion
549
10.2.
Hitting Times, Maximum Variable, and the Gambler s
Ruin Problem
553
10.3.
Variations on Brownian Motion
554
10.3.1.
Brownian Motion with Drift
554
10.3.2.
Geometric Brownian Motion
555
10.4.
Pricing Stock Options
556
10.4.1.
An Example in Options Pricing
556
10.4.2.
The Arbitrage Theorem
558
10.4.3.
The Black Scholes Option Pricing Formula
561
10.5.
White Noise
567
10.6.
Gaussian Processes
569
10.7.
Stationary and Weakly Stationary Processes
572
10.8.
Harmonic Analysis of Weakly Stationary Processes
577
Exercises
579
References
584
11.
Simulation
585
11.1.
Introduction
585
11.2.
General Techniques for Simulating Continuous
Random Variables
590
11.2.1.
The Inverse Transformation Method
590
11.2.2.
The Rejection Method
591
11.2.3.
The Hazard Rate Method
595
11.3.
Special Techniques for Simulating Continuous
Random Variables
598
11.3.1.
The Normal Distribution
598
11.3.2.
The Gamma Distribution
602
11.3.3.
The Chi-Squared Distribution
602
11.3.4.
The Beta (n, m) Distribution
603
11.3.5.
The Exponential Distribution
—
The
Von
Neumann
Algorithm
604
11.4.
Simulating from Discrete Distributions
606
11.4.1.
The Alias Method
610
11.5.
Stochastic Processes
613
11.5.1.
Simulating a Nonhomogeneous
Poisson
Process
615
11.5.2.
Simulating a Two-Dimensional
Poisson
Process
621
11.6.
Variance Reduction Techniques
624
11.6.1.
Use of Antithetic Variables
625
11.6.2.
Variance Reduction by Conditioning
629
11.6.3.
Control
Variâtes
633
11.6.4.
Importance Sampling
634
11.7.
Determining the Number of Runs
639
Exercises
640
References
648
Appendix: Solutions to Starred Exercises
649
index
687
The Seventh Edition of Ross Introduction to Probability Models represents the
continuing convergence of this best-selling book with the widening indispensability
of probability in pure and applied science.
Revised and updated, Introduction to Probability Models is particularly well suited to
those seeking an understanding of how probability theoiy and stochastic processes
apply to phenomena in such fields as engineering, management science, the physical
and social sciences, and operations research.
While retaining its focus on elementary probability and stochastic processes, this
edition s significant revisions include:
•
Nearly
600
new or updated exercises, with over
100
solutions provided
•
New derivations for the
Poisson
and nonhomogeneous
Poisson
processes
•
Optimization of a single server, general service time queue
•
Analysis of a series structure reliability model in which components enter
a state of suspended animation upon cohort failure
|
| any_adam_object | 1 |
| author | Ross, Sheldon M. 1943- |
| author_GND | (DE-588)123762235 |
| author_facet | Ross, Sheldon M. 1943- |
| author_role | aut |
| author_sort | Ross, Sheldon M. 1943- |
| author_variant | s m r sm smr |
| building | Verbundindex |
| bvnumber | BV013072892 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 R826I 2000 |
| callnumber-raw | QA273 R826i 2000 |
| callnumber-search | QA273 R826i 2000 |
| callnumber-sort | QA 3273 R826 I 42000 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 800 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)247857840 (DE-599)BVBBV013072892 |
| 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 | Mathematik |
| edition | 7. ed. |
| format | Book |
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| genre | Matériel didactique |
| genre_facet | Matériel didactique |
| id | DE-604.BV013072892 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:38Z |
| institution | BVB |
| isbn | 0125984758 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008907176 |
| oclc_num | 247857840 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29T DE-573 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-739 |
| owner_facet | DE-19 DE-BY-UBM DE-29T DE-573 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-739 |
| physical | XV, 693 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Introduction to probability models Sheldon M. Ross 7. ed. San Diego [u.a.] Acad. Press 2000 XV, 693 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilités Probabilités - Problèmes et exercices Probabilités ram Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Matériel didactique Stochastischer Prozess (DE-588)4057630-9 s Stochastisches Modell (DE-588)4057633-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 1\p DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Modell (DE-588)4039798-1 s 2\p DE-604 Mathematisches Modell (DE-588)4114528-8 s 3\p DE-604 4\p DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008907176&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008907176&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ross, Sheldon M. 1943- Introduction to probability models Probabilités Probabilités - Problèmes et exercices Probabilités ram Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Modell (DE-588)4039798-1 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4114528-8 (DE-588)4057630-9 (DE-588)4079013-7 (DE-588)4039798-1 (DE-588)4064324-4 |
| title | Introduction to probability models |
| title_auth | Introduction to probability models |
| title_exact_search | Introduction to probability models |
| title_full | Introduction to probability models Sheldon M. Ross |
| title_fullStr | Introduction to probability models Sheldon M. Ross |
| title_full_unstemmed | Introduction to probability models Sheldon M. Ross |
| title_short | Introduction to probability models |
| title_sort | introduction to probability models |
| topic | Probabilités Probabilités - Problèmes et exercices Probabilités ram Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Modell (DE-588)4039798-1 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilités Probabilités - Problèmes et exercices Stochastisches Modell Mathematisches Modell Stochastischer Prozess Wahrscheinlichkeitstheorie Modell Wahrscheinlichkeitsrechnung Matériel didactique |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008907176&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008907176&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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