The Resource A first course in probability, Sheldon Ross
A first course in probability, Sheldon Ross
Resource Information
The item A first course in probability, Sheldon Ross represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item A first course in probability, Sheldon Ross represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- Summary
-
- P. 15
- P. 52
- P. 103
- P. 169
- P. 225
- P. 288
- P. 377
- P. 426
- P. 451
- Language
- eng
- Edition
- 7th ed.
- Extent
- x, 565 p.
- Note
- "Pearson International edition" -- cover
- Contents
-
- Preface
- 1.
- Combinatorial Analysis.
- p. 1
- 1.1.
- Introduction.
- p. 1
- 1.2.
- Basic Principle of Counting.
- p. 2
- 1.3.
- Permutations.
- p. 3
- 1.4.
- Combinations.
- p. 6
- 1.5.
- Multinomial Coefficients.
- p. 10
- 1.6.
- Number of Integer Solutions of Equations*.
- p. 12
- Summary.
- p. 15
- Problems.
- p. 16
- Theoretical Exercises.
- p. 19
- Self-Test Problems and Exercises.
- p. 22
- 2.
- Axioms of Probability.
- p. 24
- 2.1.
- Introduction.
- p. 24
- 2.2.
- Sample Space and Events.
- p. 24
- 2.3.
- Axioms of Probability.
- p. 29
- 2.4.
- Some Simple Propositions.
- p. 31
- 2.5.
- Sample Spaces Having Equally Likely Outcomes.
- p. 37
- 2.6.
- Probability as a Continuous Set Function*.
- p. 49
- 2.7.
- Probability as a Measure of Belief.
- p. 53
- Summary.
- p. 54
- Problems.
- p. 55
- Theoretical Exercises.
- p. 61
- Self-Test Problems and Exercises.
- p. 63
- 3.
- Conditional Probability and Independence.
- p. 66
- 3.1.
- Introduction.
- p. 66
- 3.2.
- Conditional Probabilities.
- p. 66
- 3.3.
- Bayes' Formula.
- p. 72
- 3.4.
- Independent Events.
- p. 87
- 3.5.
- P(.[vertical bar]F) Is a Probability.
- p. 101
- Summary.
- p. 110
- Problems.
- p. 111
- Theoretical Exercises.
- p. 124
- Self-Test Problems and Exercises.
- p. 128
- 4.
- Random Variables.
- p. 132
- 4.1.
- Random Variables.
- p. 132
- 4.2.
- Discrete Random Variables.
- p. 138
- 4.3.
- Expected Value.
- p. 140
- 4.4.
- Expectation of a Function of a Random Variable.
- p. 144
- 4.5.
- Variance.
- p. 148
- 4.6.
- Bernoulli and Binomial Random Variables.
- p. 150
- 4.6.1.
- Properties of Binomial Random Variables.
- p. 155
- 4.6.2.
- Computing the Binomial Distribution Function.
- p. 158
- 4.7.
- Poisson Random Variable.
- p. 160
- 4.7.1.
- Computing the Poisson Distribution Function.
- p. 173
- 4.8.
- Other Discrete Probability Distributions.
- p. 173
- 4.8.1.
- Geometric Random Variable.
- p. 173
- 4.8.2.
- Negative Binomial Random Variable.
- p. 175
- 4.8.3.
- Hypergeometric Random Variable.
- p. 178
- 4.8.4.
- Zeta (or Zipf) Distribution.
- p. 182
- 4.9.
- Properties of the Cumulative Distribution Function.
- p. 183
- Summary.
- p. 185
- Problems.
- p. 187
- Theoretical Exercises.
- p. 197
- Self-Test Problems and Exercises.
- p. 201
- 5.
- Continuous Random Variables.
- p. 205
- 5.1.
- Introduction.
- p. 205
- 5.2.
- Expectation and Variance of Continuous Random Variables.
- p. 209
- 5.3.
- Uniform Random Variable.
- p. 214
- 5.4.
- Normal Random Variables.
- p. 218
- 5.4.1.
- Normal Approximation to the Binomial Distribution.
- p. 225
- 5.5.
- Exponential Random Variables.
- p. 230
- 5.5.1.
- Hazard Rate Functions.
- p. 234
- 5.6.
- Other Continuous Distributions.
- p. 237
- 5.6.1.
- Gamma Distribution.
- p. 237
- 5.6.2.
- Weibull Distribution.
- p. 239
- 5.6.3.
- Cauchy Distribution.
- p. 239
- 5.6.4.
- Beta Distribution.
- p. 240
- 5.7.
- Distribution of a Function of a Random Variable.
- p. 242
- Summary.
- p. 244
- Problems.
- p. 247
- Theoretical Exercises.
- p. 251
- Self-Test Problems and Exercises.
- p. 254
- 6.
- Jointly Distributed Random Variables.
- p. 258
- 6.1.
- Joint Distribution Functions.
- p. 258
- 6.2.
- Independent Random Variables.
- p. 267
- 6.3.
- Sums of Independent Random Variables.
- p. 280
- 6.4.
- Conditional Distributions: Discrete Case.
- p. 288
- 6.5.
- Conditional Distributions: Continuous Case.
- p. 291
- 6.6.
- Order Statistics.
- p. 296
- 6.7.
- Joint Probability Distribution of Functions of Random Variables.
- p. 300
- 6.8.
- Exchangeable Random Variables.
- p. 308
- Summary.
- p. 311
- Problems.
- p. 313
- Theoretical Exercises.
- p. 319
- Self-Test Problems and Exercises.
- p. 323
- 7.
- Properties of Expectation.
- p. 327
- 7.1.
- Introduction.
- p. 327
- 7.2.
- Expectation of Sums of Random Variables.
- p. 328
- 7.2.1.
- Obtaining Bounds from Expectations via the Probabilistic Method.
- p. 342
- 7.2.2.
- Maximum-Minimums Identity.
- p. 344
- 7.3.
- Moments of the Number of Events that Occur.
- p. 347
- 7.4.
- Covariance, Variance of Sums, and Correlations.
- p. 355
- 7.5.
- Conditional Expectation.
- p. 365
- 7.5.1.
- Definitions.
- p. 365
- 7.5.2.
- Computing Expectations by Conditioning.
- p. 367
- 7.5.3.
- Computing Probabilities by Conditioning.
- p. 376
- 7.5.4.
- Conditional Variance.
- p. 380
- 7.6.
- Conditional Expectation and Prediction.
- p. 382
- 7.7.
- Moment Generating Functions.
- p. 387
- 7.7.1.
- Joint Moment Generating Functions.
- p. 397
- 7.8.
- Additional Properties of Normal Random Variables.
- p. 399
- 7.8.1.
- Multivariate Normal Distribution.
- p. 399
- 7.8.2.
- Joint Distribution of the Sample Mean and Sample Variance.
- p. 402
- 7.9.
- General Definition of Expectation.
- p. 404
- Summary.
- p. 405
- Problems.
- p. 408
- Theoretical Exercises.
- p. 418
- Self-Test Problems and Exercises.
- p. 426
- 8.
- Limit Theorems.
- p. 430
- 8.1.
- Introduction.
- p. 430
- 8.2.
- Chebyshev's Inequality and the Weak Law of Large Numbers.
- p. 430
- 8.3.
- Central Limit Theorem.
- p. 434
- 8.4.
- Strong Law of Large Numbers.
- p. 443
- 8.5.
- Other Inequalities.
- p. 445
- 8.6.
- Bounding The Error Probability.
- p. 454
- Summary.
- p. 456
- Problems.
- p. 457
- Theoretical Exercises.
- p. 459
- Self-Test Problems and Exercises.
- p. 461
- 9.
- Additional Topics in Probability.
- p. 463
- 9.1.
- Poisson Process.
- p. 463
- 9.2.
- Markov Chains.
- p. 466
- 9.3.
- Surprise, Uncertainty, and Entropy.
- p. 472
- 9.4.
- Coding Theory and Entropy.
- p. 476
- Summary.
- p. 483
- .
- Theoretical Exercises.
- p. 484
- .
- Self-Test Problems and Exercises.
- p. 485
- 10.
- Simulation.
- p. 487
- 10.1.
- Introduction.
- p. 487
- 10.2.
- General Techniques for Simulating Continuous Random Variables.
- p. 490
- 10.2.1.
- Inverse Transformation Method.
- p. 490
- 10.2.2.
- Rejection Method.
- p. 491
- 10.3.
- Simulating from Discrete Distributions.
- p. 497
- 10.4.
- Variance Reduction Techniques.
- p. 499
- 10.4.1.
- Use of Antithetic Variables.
- p. 500
- 10.4.2.
- Variance Reduction by Conditioning.
- p. 501
- 10.4.3.
- Control Variates.
- p. 503
- Summary.
- p. 503
- .
- Problems.
- p. 504
- .
- Self-Test Problems and Exercises.
- p. 506
- .
- Appendices
- A.
- Answers to Selected Problems.
- p. 508
- B.
- Solutions to Self-Test Problems and Exercises.
- p. 511
- .
- Index.
- p. 561
- Isbn
- 9780132018173
- Label
- A first course in probability
- Title
- A first course in probability
- Statement of responsibility
- Sheldon Ross
- Language
- eng
- Summary
-
- P. 15
- P. 52
- P. 103
- P. 169
- P. 225
- P. 288
- P. 377
- P. 426
- P. 451
- Cataloging source
- DLC
- http://library.link/vocab/creatorName
- Ross, Sheldon M
- Index
- index present
- Language note
- English
- Literary form
- non fiction
- http://library.link/vocab/subjectName
- Probabilities
- Label
- A first course in probability, Sheldon Ross
- Note
- "Pearson International edition" -- cover
- Bibliography note
- Includes index
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Preface
- 1.
- Combinatorial Analysis.
- p. 1
- 1.1.
- Introduction.
- p. 1
- 1.2.
- Basic Principle of Counting.
- p. 2
- 1.3.
- Permutations.
- p. 3
- 1.4.
- Combinations.
- p. 6
- 1.5.
- Multinomial Coefficients.
- p. 10
- 1.6.
- Number of Integer Solutions of Equations*.
- p. 12
- Summary.
- p. 15
- Problems.
- p. 16
- Theoretical Exercises.
- p. 19
- Self-Test Problems and Exercises.
- p. 22
- 2.
- Axioms of Probability.
- p. 24
- 2.1.
- Introduction.
- p. 24
- 2.2.
- Sample Space and Events.
- p. 24
- 2.3.
- Axioms of Probability.
- p. 29
- 2.4.
- Some Simple Propositions.
- p. 31
- 2.5.
- Sample Spaces Having Equally Likely Outcomes.
- p. 37
- 2.6.
- Probability as a Continuous Set Function*.
- p. 49
- 2.7.
- Probability as a Measure of Belief.
- p. 53
- Summary.
- p. 54
- Problems.
- p. 55
- Theoretical Exercises.
- p. 61
- Self-Test Problems and Exercises.
- p. 63
- 3.
- Conditional Probability and Independence.
- p. 66
- 3.1.
- Introduction.
- p. 66
- 3.2.
- Conditional Probabilities.
- p. 66
- 3.3.
- Bayes' Formula.
- p. 72
- 3.4.
- Independent Events.
- p. 87
- 3.5.
- P(.[vertical bar]F) Is a Probability.
- p. 101
- Summary.
- p. 110
- Problems.
- p. 111
- Theoretical Exercises.
- p. 124
- Self-Test Problems and Exercises.
- p. 128
- 4.
- Random Variables.
- p. 132
- 4.1.
- Random Variables.
- p. 132
- 4.2.
- Discrete Random Variables.
- p. 138
- 4.3.
- Expected Value.
- p. 140
- 4.4.
- Expectation of a Function of a Random Variable.
- p. 144
- 4.5.
- Variance.
- p. 148
- 4.6.
- Bernoulli and Binomial Random Variables.
- p. 150
- 4.6.1.
- Properties of Binomial Random Variables.
- p. 155
- 4.6.2.
- Computing the Binomial Distribution Function.
- p. 158
- 4.7.
- Poisson Random Variable.
- p. 160
- 4.7.1.
- Computing the Poisson Distribution Function.
- p. 173
- 4.8.
- Other Discrete Probability Distributions.
- p. 173
- 4.8.1.
- Geometric Random Variable.
- p. 173
- 4.8.2.
- Negative Binomial Random Variable.
- p. 175
- 4.8.3.
- Hypergeometric Random Variable.
- p. 178
- 4.8.4.
- Zeta (or Zipf) Distribution.
- p. 182
- 4.9.
- Properties of the Cumulative Distribution Function.
- p. 183
- Summary.
- p. 185
- Problems.
- p. 187
- Theoretical Exercises.
- p. 197
- Self-Test Problems and Exercises.
- p. 201
- 5.
- Continuous Random Variables.
- p. 205
- 5.1.
- Introduction.
- p. 205
- 5.2.
- Expectation and Variance of Continuous Random Variables.
- p. 209
- 5.3.
- Uniform Random Variable.
- p. 214
- 5.4.
- Normal Random Variables.
- p. 218
- 5.4.1.
- Normal Approximation to the Binomial Distribution.
- p. 225
- 5.5.
- Exponential Random Variables.
- p. 230
- 5.5.1.
- Hazard Rate Functions.
- p. 234
- 5.6.
- Other Continuous Distributions.
- p. 237
- 5.6.1.
- Gamma Distribution.
- p. 237
- 5.6.2.
- Weibull Distribution.
- p. 239
- 5.6.3.
- Cauchy Distribution.
- p. 239
- 5.6.4.
- Beta Distribution.
- p. 240
- 5.7.
- Distribution of a Function of a Random Variable.
- p. 242
- Summary.
- p. 244
- Problems.
- p. 247
- Theoretical Exercises.
- p. 251
- Self-Test Problems and Exercises.
- p. 254
- 6.
- Jointly Distributed Random Variables.
- p. 258
- 6.1.
- Joint Distribution Functions.
- p. 258
- 6.2.
- Independent Random Variables.
- p. 267
- 6.3.
- Sums of Independent Random Variables.
- p. 280
- 6.4.
- Conditional Distributions: Discrete Case.
- p. 288
- 6.5.
- Conditional Distributions: Continuous Case.
- p. 291
- 6.6.
- Order Statistics.
- p. 296
- 6.7.
- Joint Probability Distribution of Functions of Random Variables.
- p. 300
- 6.8.
- Exchangeable Random Variables.
- p. 308
- Summary.
- p. 311
- Problems.
- p. 313
- Theoretical Exercises.
- p. 319
- Self-Test Problems and Exercises.
- p. 323
- 7.
- Properties of Expectation.
- p. 327
- 7.1.
- Introduction.
- p. 327
- 7.2.
- Expectation of Sums of Random Variables.
- p. 328
- 7.2.1.
- Obtaining Bounds from Expectations via the Probabilistic Method.
- p. 342
- 7.2.2.
- Maximum-Minimums Identity.
- p. 344
- 7.3.
- Moments of the Number of Events that Occur.
- p. 347
- 7.4.
- Covariance, Variance of Sums, and Correlations.
- p. 355
- 7.5.
- Conditional Expectation.
- p. 365
- 7.5.1.
- Definitions.
- p. 365
- 7.5.2.
- Computing Expectations by Conditioning.
- p. 367
- 7.5.3.
- Computing Probabilities by Conditioning.
- p. 376
- 7.5.4.
- Conditional Variance.
- p. 380
- 7.6.
- Conditional Expectation and Prediction.
- p. 382
- 7.7.
- Moment Generating Functions.
- p. 387
- 7.7.1.
- Joint Moment Generating Functions.
- p. 397
- 7.8.
- Additional Properties of Normal Random Variables.
- p. 399
- 7.8.1.
- Multivariate Normal Distribution.
- p. 399
- 7.8.2.
- Joint Distribution of the Sample Mean and Sample Variance.
- p. 402
- 7.9.
- General Definition of Expectation.
- p. 404
- Summary.
- p. 405
- Problems.
- p. 408
- Theoretical Exercises.
- p. 418
- Self-Test Problems and Exercises.
- p. 426
- 8.
- Limit Theorems.
- p. 430
- 8.1.
- Introduction.
- p. 430
- 8.2.
- Chebyshev's Inequality and the Weak Law of Large Numbers.
- p. 430
- 8.3.
- Central Limit Theorem.
- p. 434
- 8.4.
- Strong Law of Large Numbers.
- p. 443
- 8.5.
- Other Inequalities.
- p. 445
- 8.6.
- Bounding The Error Probability.
- p. 454
- Summary.
- p. 456
- Problems.
- p. 457
- Theoretical Exercises.
- p. 459
- Self-Test Problems and Exercises.
- p. 461
- 9.
- Additional Topics in Probability.
- p. 463
- 9.1.
- Poisson Process.
- p. 463
- 9.2.
- Markov Chains.
- p. 466
- 9.3.
- Surprise, Uncertainty, and Entropy.
- p. 472
- 9.4.
- Coding Theory and Entropy.
- p. 476
- Summary.
- p. 483
- .
- Theoretical Exercises.
- p. 484
- .
- Self-Test Problems and Exercises.
- p. 485
- 10.
- Simulation.
- p. 487
- 10.1.
- Introduction.
- p. 487
- 10.2.
- General Techniques for Simulating Continuous Random Variables.
- p. 490
- 10.2.1.
- Inverse Transformation Method.
- p. 490
- 10.2.2.
- Rejection Method.
- p. 491
- 10.3.
- Simulating from Discrete Distributions.
- p. 497
- 10.4.
- Variance Reduction Techniques.
- p. 499
- 10.4.1.
- Use of Antithetic Variables.
- p. 500
- 10.4.2.
- Variance Reduction by Conditioning.
- p. 501
- 10.4.3.
- Control Variates.
- p. 503
- Summary.
- p. 503
- .
- Problems.
- p. 504
- .
- Self-Test Problems and Exercises.
- p. 506
- .
- Appendices
- A.
- Answers to Selected Problems.
- p. 508
- B.
- Solutions to Self-Test Problems and Exercises.
- p. 511
- .
- Index.
- p. 561
- Control code
- ocm59401216
- Dimensions
- 25 cm.
- Edition
- 7th ed.
- Extent
- x, 565 p.
- Isbn
- 9780132018173
- Lccn
- 2005047691
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
- Other physical details
- ill.
- Label
- A first course in probability, Sheldon Ross
- Note
- "Pearson International edition" -- cover
- Bibliography note
- Includes index
- Carrier category
- volume
- Carrier category code
-
- nc
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Preface
- 1.
- Combinatorial Analysis.
- p. 1
- 1.1.
- Introduction.
- p. 1
- 1.2.
- Basic Principle of Counting.
- p. 2
- 1.3.
- Permutations.
- p. 3
- 1.4.
- Combinations.
- p. 6
- 1.5.
- Multinomial Coefficients.
- p. 10
- 1.6.
- Number of Integer Solutions of Equations*.
- p. 12
- Summary.
- p. 15
- Problems.
- p. 16
- Theoretical Exercises.
- p. 19
- Self-Test Problems and Exercises.
- p. 22
- 2.
- Axioms of Probability.
- p. 24
- 2.1.
- Introduction.
- p. 24
- 2.2.
- Sample Space and Events.
- p. 24
- 2.3.
- Axioms of Probability.
- p. 29
- 2.4.
- Some Simple Propositions.
- p. 31
- 2.5.
- Sample Spaces Having Equally Likely Outcomes.
- p. 37
- 2.6.
- Probability as a Continuous Set Function*.
- p. 49
- 2.7.
- Probability as a Measure of Belief.
- p. 53
- Summary.
- p. 54
- Problems.
- p. 55
- Theoretical Exercises.
- p. 61
- Self-Test Problems and Exercises.
- p. 63
- 3.
- Conditional Probability and Independence.
- p. 66
- 3.1.
- Introduction.
- p. 66
- 3.2.
- Conditional Probabilities.
- p. 66
- 3.3.
- Bayes' Formula.
- p. 72
- 3.4.
- Independent Events.
- p. 87
- 3.5.
- P(.[vertical bar]F) Is a Probability.
- p. 101
- Summary.
- p. 110
- Problems.
- p. 111
- Theoretical Exercises.
- p. 124
- Self-Test Problems and Exercises.
- p. 128
- 4.
- Random Variables.
- p. 132
- 4.1.
- Random Variables.
- p. 132
- 4.2.
- Discrete Random Variables.
- p. 138
- 4.3.
- Expected Value.
- p. 140
- 4.4.
- Expectation of a Function of a Random Variable.
- p. 144
- 4.5.
- Variance.
- p. 148
- 4.6.
- Bernoulli and Binomial Random Variables.
- p. 150
- 4.6.1.
- Properties of Binomial Random Variables.
- p. 155
- 4.6.2.
- Computing the Binomial Distribution Function.
- p. 158
- 4.7.
- Poisson Random Variable.
- p. 160
- 4.7.1.
- Computing the Poisson Distribution Function.
- p. 173
- 4.8.
- Other Discrete Probability Distributions.
- p. 173
- 4.8.1.
- Geometric Random Variable.
- p. 173
- 4.8.2.
- Negative Binomial Random Variable.
- p. 175
- 4.8.3.
- Hypergeometric Random Variable.
- p. 178
- 4.8.4.
- Zeta (or Zipf) Distribution.
- p. 182
- 4.9.
- Properties of the Cumulative Distribution Function.
- p. 183
- Summary.
- p. 185
- Problems.
- p. 187
- Theoretical Exercises.
- p. 197
- Self-Test Problems and Exercises.
- p. 201
- 5.
- Continuous Random Variables.
- p. 205
- 5.1.
- Introduction.
- p. 205
- 5.2.
- Expectation and Variance of Continuous Random Variables.
- p. 209
- 5.3.
- Uniform Random Variable.
- p. 214
- 5.4.
- Normal Random Variables.
- p. 218
- 5.4.1.
- Normal Approximation to the Binomial Distribution.
- p. 225
- 5.5.
- Exponential Random Variables.
- p. 230
- 5.5.1.
- Hazard Rate Functions.
- p. 234
- 5.6.
- Other Continuous Distributions.
- p. 237
- 5.6.1.
- Gamma Distribution.
- p. 237
- 5.6.2.
- Weibull Distribution.
- p. 239
- 5.6.3.
- Cauchy Distribution.
- p. 239
- 5.6.4.
- Beta Distribution.
- p. 240
- 5.7.
- Distribution of a Function of a Random Variable.
- p. 242
- Summary.
- p. 244
- Problems.
- p. 247
- Theoretical Exercises.
- p. 251
- Self-Test Problems and Exercises.
- p. 254
- 6.
- Jointly Distributed Random Variables.
- p. 258
- 6.1.
- Joint Distribution Functions.
- p. 258
- 6.2.
- Independent Random Variables.
- p. 267
- 6.3.
- Sums of Independent Random Variables.
- p. 280
- 6.4.
- Conditional Distributions: Discrete Case.
- p. 288
- 6.5.
- Conditional Distributions: Continuous Case.
- p. 291
- 6.6.
- Order Statistics.
- p. 296
- 6.7.
- Joint Probability Distribution of Functions of Random Variables.
- p. 300
- 6.8.
- Exchangeable Random Variables.
- p. 308
- Summary.
- p. 311
- Problems.
- p. 313
- Theoretical Exercises.
- p. 319
- Self-Test Problems and Exercises.
- p. 323
- 7.
- Properties of Expectation.
- p. 327
- 7.1.
- Introduction.
- p. 327
- 7.2.
- Expectation of Sums of Random Variables.
- p. 328
- 7.2.1.
- Obtaining Bounds from Expectations via the Probabilistic Method.
- p. 342
- 7.2.2.
- Maximum-Minimums Identity.
- p. 344
- 7.3.
- Moments of the Number of Events that Occur.
- p. 347
- 7.4.
- Covariance, Variance of Sums, and Correlations.
- p. 355
- 7.5.
- Conditional Expectation.
- p. 365
- 7.5.1.
- Definitions.
- p. 365
- 7.5.2.
- Computing Expectations by Conditioning.
- p. 367
- 7.5.3.
- Computing Probabilities by Conditioning.
- p. 376
- 7.5.4.
- Conditional Variance.
- p. 380
- 7.6.
- Conditional Expectation and Prediction.
- p. 382
- 7.7.
- Moment Generating Functions.
- p. 387
- 7.7.1.
- Joint Moment Generating Functions.
- p. 397
- 7.8.
- Additional Properties of Normal Random Variables.
- p. 399
- 7.8.1.
- Multivariate Normal Distribution.
- p. 399
- 7.8.2.
- Joint Distribution of the Sample Mean and Sample Variance.
- p. 402
- 7.9.
- General Definition of Expectation.
- p. 404
- Summary.
- p. 405
- Problems.
- p. 408
- Theoretical Exercises.
- p. 418
- Self-Test Problems and Exercises.
- p. 426
- 8.
- Limit Theorems.
- p. 430
- 8.1.
- Introduction.
- p. 430
- 8.2.
- Chebyshev's Inequality and the Weak Law of Large Numbers.
- p. 430
- 8.3.
- Central Limit Theorem.
- p. 434
- 8.4.
- Strong Law of Large Numbers.
- p. 443
- 8.5.
- Other Inequalities.
- p. 445
- 8.6.
- Bounding The Error Probability.
- p. 454
- Summary.
- p. 456
- Problems.
- p. 457
- Theoretical Exercises.
- p. 459
- Self-Test Problems and Exercises.
- p. 461
- 9.
- Additional Topics in Probability.
- p. 463
- 9.1.
- Poisson Process.
- p. 463
- 9.2.
- Markov Chains.
- p. 466
- 9.3.
- Surprise, Uncertainty, and Entropy.
- p. 472
- 9.4.
- Coding Theory and Entropy.
- p. 476
- Summary.
- p. 483
- .
- Theoretical Exercises.
- p. 484
- .
- Self-Test Problems and Exercises.
- p. 485
- 10.
- Simulation.
- p. 487
- 10.1.
- Introduction.
- p. 487
- 10.2.
- General Techniques for Simulating Continuous Random Variables.
- p. 490
- 10.2.1.
- Inverse Transformation Method.
- p. 490
- 10.2.2.
- Rejection Method.
- p. 491
- 10.3.
- Simulating from Discrete Distributions.
- p. 497
- 10.4.
- Variance Reduction Techniques.
- p. 499
- 10.4.1.
- Use of Antithetic Variables.
- p. 500
- 10.4.2.
- Variance Reduction by Conditioning.
- p. 501
- 10.4.3.
- Control Variates.
- p. 503
- Summary.
- p. 503
- .
- Problems.
- p. 504
- .
- Self-Test Problems and Exercises.
- p. 506
- .
- Appendices
- A.
- Answers to Selected Problems.
- p. 508
- B.
- Solutions to Self-Test Problems and Exercises.
- p. 511
- .
- Index.
- p. 561
- Control code
- ocm59401216
- Dimensions
- 25 cm.
- Edition
- 7th ed.
- Extent
- x, 565 p.
- Isbn
- 9780132018173
- Lccn
- 2005047691
- Media category
- unmediated
- Media MARC source
- rdamedia
- Media type code
-
- n
- Other physical details
- ill.
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/A-first-course-in-probability-Sheldon/TD-n4-Y_dNk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/A-first-course-in-probability-Sheldon/TD-n4-Y_dNk/">A first course in probability, Sheldon Ross</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
