UID:
almahu_9948026676902882
Umfang:
1 online resource (347 p.)
ISBN:
0-85709-947-7
Serie:
Mathematics, Statistics, Operations Research
Inhalt:
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 n
Anmerkung:
Includes index.
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"Republished, with corrections, in 2005"--T.p. verso.
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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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7.2 FUNCTIONS OF DISCRETE RANDOM VARIABLES7.3 FUNCTIONS OF CONTINUOUS RANDOM VARIABLES; 7.4 NON-MONOTONE FUNCTION; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 8 Bivariate Distributions; 8.1 DISCRETE BIVARIATE DISTRIBUTIONS; 8.2 THE TRINOMIAL DISTRIBUTION; 8.3 CONTINUOUS BIVARIATE DISTRIBUTIONS; 8.4 THE BIVARIATE NORMAL DISTRIBUTION; 8.5 RANDOM PARAMETERS; REFERENCES; BRIEF SOLUTIONS AND COMMENTS ON THE PROBLEMS; 9 Expectation of a Random Variable; 9.1 ΙΝΤRODUCTION; 9.2 THE STANDARD DISTRIBUTIONS; 9.3 EXPECTATION AND CHOICE OF ACTION; 9.4 EXPECTATION OF A FUNCTION OF A RANDOM VARIABLE
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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
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12 Moments of Bivariate Distributions
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English
Weitere Ausg.:
ISBN 1-904275-19-2
Sprache:
Englisch
