| Description |
1 online resource (345 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Mathematics, statistics, and operational research |
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Ellis Horwood series in mathematics and its applications. Statistics and operational research.
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| Note |
"Republished, with corrections, in 2005"--Title page verso |
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Includes index. |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Summary |
This undergraduate text distils the wisdom of an experienced teacher and yields, to the mutual advantage of students and their instructors, a sound and stimulating introduction to probability theory. The accent is on its essential role in statistical theory and practice, built on the use of illustrative examples and the solution of problems from typical examination papers. Mathematically-friendly for first and second year undergraduate students, the book is also a reference source for workers in a wide range of disciplines who are aware that even the simpler aspects of probability theory are not simple. Provides a sound and stimulating introduction to probability theoryPlaces emphasis on the role of probability theory in statistical theory and practice, built on the use of illustrative examples and the solution of problems from typical examination papers. |
| Contents |
Cover; PROBABILITY AND RANDOM VARIABLES; Copyright; Contents; Preface; Acknowledgements; 1 Introduction; 2 Probability; 2.1 AXIOMATIC APPROACH; 2.2 SAMPLE SPACE; 2.3 COMBINATION OF EVENTS; 2.4 VENN DIAGRAMS; 2.5 AXIOMS FOR PROBABILITIES FOR A SAMPLE SPACE WITH A FINITE NUMBER OF POINTS; 2.6 SETS AND EVENTS; 2.7 COUNTING METHODS; 2.8 PERMUTATIONS; 2.9 COMBINATIONS; 2.10 ARRANGEMENTS IN A ROW; 2.11 RANDOM SAMPLING; 2.12 COMBINATORIAL IDENTITIES; 2.13 THE QUANTITIES (n r) AND THE BINOMIAL THEOREM; 2.14 MULTINOMIAL EXPANSION; 2.15 RUNS; REFERENCE; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS |
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3 Conditional Probability and Independence3.1 INTRODUCTION; 3.2 EVALUATING PROBABILITIES; 3.3 APPLICATIONS; 3.4 CONDITIONAL PROBABILITIES; 3.5 INDEPENDENT EVENTS; 3.6 SAMPLING WITH REPLACEMENT; 3.7 THE PROBABILITY OF AT LEAST ONE EVENT; 3.8 INFINITE SEQUENCE OF INDEPENDENT TRIALS; REFERENCE; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 4 Random Variables; 4.1 INFINITE SAMPLE SPACES; 4.2 RANDOM VARIABLES; 4.3 DISCRETE AND CONTINUOUS RANDOM VARIABLES; 4.4 THE BERNOULLI DISTRIBUTION; 4.5 THE BINOMIAL DISTRIBUTION; 4.6 THE HYPERGEOMETRIC DISTRIBUTION; 4.7 THE GEOMETRIC DISTRIBUTION |
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4.8 THE NEGATIVE BINOMIAL DISTRIBUTION4.9 THE POISSON DISTRIBUTION; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 5 Continuous Distributions; 5.1 RECTANGULAR DISTRIBUTION; 5.2 EXPONENTIAL DISTRIBUTION; 5.3 RANDOM STREAM OF EVENTS; 5.4 THE GAMMA DISTRIBUTION; 5.5 THE NORMAL DISTRIBUTION; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 6 Distribution Function; 6.1 THE MODE; 6.2 THE MEDIAN; 6.3 CUMULATIVE DISTIBUTION FUNCTION; 6.4 SAMPLING A DISTRIBUTION; 6.5 EMPIRICAL DISTRIBUTION FUNCTION; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 7 Functions of Random Variables; 7.1 INTRODUCTION |
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9.5 APPLICATIONSBRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 10 Variance of a Random Variable; 10.1 VARIANCE AND PROBABILITY; 10.2 THE STANDARD DISTRIBUTIONS; 10.3 AN APPLICATION OF TCHEBYCHEV'S INEQUALITY; 10.4 MEAN AND VARIANCE OF A FUNCTION OF A CONTINUOUS RANDOM VARIABLE; 10.5 TRUNCATED DISTRIBUTIONS; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 11 Moment Generating Functions; 11.1 THE MOMENTS OF A DISTRIBUTION; 11.2 SYMMETRY AND FLATNESS; 11.3 MOMENT GENERATING FUNCTIONS; 11.4 FUNCTION OF A RANDOM VARIABLE; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS |
| Subject |
Probabilities.
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Random variables.
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Probability |
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Probabilités.
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Variables aléatoires.
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probability.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Probabilities
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Random variables
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| Indexed Term |
Probabilities & statistical mathematics |
| Other Form: |
Print version: Beaumont, G.P. (Geoffrey P.). Probability and random variables 1904275192 (DLC) 2005279299 (OCoLC)60330681 |
| ISBN |
9780857099471 (electronic bk.) |
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0857099477 (electronic bk.) |
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1904275192 |
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9781904275190 |
| Standard No. |
CHNEW 001011797 |
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DEBBG BV042317199 |
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DEBSZ 414270770 |
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GBVCP 813168627 |
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