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Record Nr. |
UNINA9910141253303321 |
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Autore |
Olofsson Peter <1963-> |
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Titolo |
Probability, statistics, and stochastic processes / / Peter Olofsson, Mikael Andersson |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley, 2012 |
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ISBN |
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9786613622280 |
9781280592454 |
1280592451 |
9781118231296 |
1118231295 |
9781118231302 |
1118231309 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (574 p.) |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Stochastic processes |
Probabilities |
Mathematical statistics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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PROBABILITY, STATISTICS, AND STOCHASTIC PROCESSES; CONTENTS; Preface; Preface to the First Edition; 1 Basic Probability Theory; 1.1 Introduction; 1.2 Sample Spaces and Events; 1.3 The Axioms of Probability; 1.4 Finite Sample Spaces and Combinatorics; 1.4.1 Combinatorics; 1.5 Conditional Probability and Independence; 1.5.1 Independent Events; 1.6 The Law of Total Probability and Bayes' Formula; 1.6.1 Bayes' Formula; 1.6.2 Genetics and Probability; 1.6.3 Recursive Methods; Problems; 2 Random Variables; 2.1 Introduction; 2.2 Discrete Random Variables; 2.3 Continuous Random Variables |
2.3.1 The Uniform Distribution2.3.2 Functions of Random Variables; 2.4 Expected Value and Variance; 2.4.1 The Expected Value of a Function of a Random Variable; 2.4.2 Variance of a Random Variable; |
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2.5 Special Discrete Distributions; 2.5.1 Indicators; 2.5.2 The Binomial Distribution; 2.5.3 The Geometric Distribution; 2.5.4 The Poisson Distribution; 2.5.5 The Hypergeometric Distribution; 2.5.6 Describing Data Sets; 2.6 The Exponential Distribution; 2.7 The Normal Distribution; 2.8 Other Distributions; 2.8.1 The Lognormal Distribution; 2.8.2 The Gamma Distribution; 2.8.3 The Cauchy Distribution |
2.8.4 Mixed Distributions2.9 Location Parameters; 2.10 The Failure Rate Function; 2.10.1 Uniqueness of the Failure Rate Function; Problems; 3 Joint Distributions; 3.1 Introduction; 3.2 The Joint Distribution Function; 3.3 Discrete Random Vectors; 3.4 Jointly Continuous Random Vectors; 3.5 Conditional Distributions and Independence; 3.5.1 Independent Random Variables; 3.6 Functions of Random Vectors; 3.6.1 Real-Valued Functions of Random Vectors; 3.6.2 The Expected Value and Variance of a Sum; 3.6.3 Vector-Valued Functions of Random Vectors; 3.7 Conditional Expectation |
3.7.1 Conditional Expectation as a Random Variable3.7.2 Conditional Expectation and Prediction; 3.7.3 Conditional Variance; 3.7.4 Recursive Methods; 3.8 Covariance and Correlation; 3.8.1 The Correlation Coefficient; 3.9 The Bivariate Normal Distribution; 3.10 Multidimensional Random Vectors; 3.10.1 Order Statistics; 3.10.2 Reliability Theory; 3.10.3 The Multinomial Distribution; 3.10.4 The Multivariate Normal Distribution; 3.10.5 Convolution; 3.11 Generating Functions; 3.11.1 The Probability Generating Function; 3.11.2 The Moment Generating Function; 3.12 The Poisson Process |
3.12.1 Thinning and SuperpositionProblems; 4 Limit Theorems; 4.1 Introduction; 4.2 The Law of Large Numbers; 4.3 The Central Limit Theorem; 4.3.1 The Delta Method; 4.4 Convergence in Distribution; 4.4.1 Discrete Limits; 4.4.2 Continuous Limits; Problems; 5 Simulation; 5.1 Introduction; 5.2 Random Number Generation; 5.3 Simulation of Discrete Distributions; 5.4 Simulation of Continuous Distributions; 5.5 Miscellaneous; Problems; 6 Statistical Inference; 6.1 Introduction; 6.2 Point Estimators; 6.2.1 Estimating the Variance; 6.3 Confidence Intervals |
6.3.1 Confidence Interval for the Mean in the Normal Distribution with Known Variance |
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Sommario/riassunto |
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Praise for the First Edition "". . . an excellent textbook . . . well organized and neatly written.""-Mathematical Reviews "". . . amazingly interesting . . .""-Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introdu |
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