Author | Blom, Gunnar. author |
---|---|
Title | Probability and Statistics [electronic resource] : Theory and Applications / by Gunnar Blom |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3566-8 |
Descript | XI, 356 p. online resource |
1 Introduction to Probability Theory -- 1.1. On the Usefulness of Probability Theory -- 1.2. Models, Especially Random Models -- 1.3. Some Historical Notes -- 2 Elements of Probability Theory -- 2.1. Introduction -- 2.2. Events -- 2.3. Probabilities in a General Sample Space -- 2.4. Probabilities in Discrete Sample Spaces -- 2.5. Conditional Probability -- 2.6. Independent Events -- 2.7. Some Theorems in Combinatorics -- 2.8. Some Classical Problems of Probability1 -- 3 One-Dimensional Random Variables -- 3.1. Introduction -- 3.2. General Description of Random Variables -- 3.3. Distribution Function -- 3.4. Discrete Random Variables -- 3.5. Some Discrete Distributions -- 3.6. Continuous Random Variables -- 3.7. Some Continuous Distributions -- 3.8. Relationship Between Discrete and Continuous Distributions -- 3.9. Mixtures of Random Variables -- 4 Multidimensional Random Variables -- 4.1. Introduction -- 4.2. General Considerations -- 4.3. Discrete Two-Dimensional Random Variables -- 4.4. Continuous Two-Dimensional Random Variables -- 4.5. Independent Random Variables -- 4.6. Some Classical Problems of Probability1 -- 5 Functions of Random Variables -- 5.1. Introduction -- 5.2. A Single Function of a Random Variable -- 5.3. Sums of Random Variables -- 5.4. Largest Value and Smallest Value -- 5.5. Ratio of Random Variables -- 6 Expectations -- 6.1. Introduction -- 6.2. Definition and Simple Properties -- 6.3. Measures of Location and Dispersion -- 6.4. Measures of Dependence -- 7 More About Expectations -- 7.1. Introduction -- 7.2. Product, Sum and Linear Combination -- 7.3. Arithmetic Mean. Law of Large Numbers -- 7.4. Gaussโs Approximation Formulae -- 7.5. Some Classical Problems of Probability1 -- 8 The Normal Distribution -- 8.1. Introduction -- 8.2. Some General Facts About the Normal Distribution -- 8.3. Standard Normal Distribution -- 8.4. General Normal Distribution -- 8.5. Sums and Linear Combinations of Normally Distributed Random Variables -- 8.6. The Central Limit Theorem -- 8.7. Lognormal Distribution -- 9 The Binomial and Related Distributions -- 9.1. Introduction -- 9.2. The Binomial Distribution -- 9.3. The Hypergeometric Distribution -- 9.4. The Poisson Distribution -- 9.5. The Multinomial Distribution -- 10 Introduction to Statistical Theory -- 10.1. Introduction -- 10.2. Statistical Investigations -- 10.3. Examples of Sampling Investigations -- 10.4. Main Problems in Statistical Theory -- 10.5. Some Historical Notes -- 11 Descriptive Statistics -- 11.1. Introduction -- 11.2. Tabulation and Graphical Presentation -- 11.3. Measures of Location and Dispersion -- 11.4. Terminology -- 11.5. Numerical Computation -- 12 Point Estimation -- 12.1. Introduction -- 12.2. General Ideas -- 12.3. Estimation of Mean and Variance -- 12.4. The Method of Maximum Likelihood -- 12.5. The Method of Least Squares -- 12.6. Application to the Normal Distribution -- 12.7. Application to the Binomial and Related Distributions -- 12.8. Standard Error of an Estimate -- 12.9. Graphical Method for Estimating Parameters -- 12.10. Estimation of Probability Function, Density Function and Distribution Function1 -- 12.11. Parameter with Prior Distribution1 -- 13 Interval Estimation -- 13.1. Introduction -- 13.2. Some Ideas About Interval Estimates -- 13.3. General Method -- 13.4. Application to the Normal Distribution -- 13.5. Using the Normal Approximation -- 13.6. Application to the Binomial and Related Distributions -- 14 Testing Hypotheses -- 14.1. Introduction -- 14.2. An Example of Hypothesis Testing -- 14.3. General Method -- 14.4. Relation Between Tests of Hypotheses and Interval Estimation -- 14.5. Application to the Normal Distribution -- 14.6. Using the Normal Approximation -- 14.7. Application to the Binomial and Related Distributions -- 14.8. The Practical Value of Tests of Significance -- 14.9. Repeated Tests of Significance -- 15 Linear Regression -- 15.1. Introduction -- 15.2. A Model for Simple Linear Regression -- 15.3. Point Estimates -- 15.4. Interval Estimates -- 15.5. Several y-Values for Each x-Value -- 15.6. Various Remarks -- 16 Planning Statistical Investigations -- 16.1. Introduction -- 16.2. General Remarks About Planning -- 16.3. Noncomparative Investigations -- 16.4. Comparative Investigations -- 16.5. Final Remarks -- Appendix: How to Handle Random Numbers -- Selected Exercises -- References -- Tables -- Answers to Exercises -- Answers to Selected Exercises