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Probability and random variables /
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 illustra...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Chichester, West Sussex England :
Ellis Horwood,
2005.
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| Series: | Ellis Horwood series in mathematics and its applications. Statistics and operational research.
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| Subjects: | |
| Online Access: | Texto completo |
Table of 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
- 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
- 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
- 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