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Probability theory and mathematical statistics for engineers /
Probability Theory and Mathematical Statistics for Engineers.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Oxford ; New York :
Pergamon Press,
1984.
|
| Edición: | First edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Probability Theoryand Mathematical Statisticsfor Engineers; Copyright Page; PREFACE; Table of Contents; CHAPTER 1. PROBABILITIES OF EVENTS; 1.1. Random phenomena; 1.2. Statistical approach to the description of random phenomena; 1.3. Direct evaluation of probabilities; 1.4. Operations with events; 1.5. Axioms of probability theory; 1.6. Conditional probabilities; 1.7. Probabilities of complex events; 1.8. Repeated trials; 1.9. Poisson distribution; CHAPTER 2. RANDOM VARIABLES; 2.1. General definitions. Discrete random variables.
- 2.2. Continuous random variables. Density of a random variable2.3. Generalization of the density concept; 2.4. Distribution function; 2.5. Entropy of a distribution; CHAPTER 3. NUMERICAL CHARACTERISTICSOF RANDOM VARIABLES; 3.1. Expectation; 3.2. Characteristics of the scatter; 3.3. Second-order moments of random vectors; 3.4. Canonical expansions of random vectors; 3.5. Other numerical characteristics of random variables; 3.6. One-dimensional normal distribution; CHAPTER 4. PROJECTIONS OF RANDOM VECTORSAND THEIR DISTRIBUTIONS; 4.1. Distributions of projections of a random vector.
- 4.2. Conditional distributions of projections of a random vector4.3. Conditional numerical characteristics; 4.4. Characteristic functions of random variables; 4.5. Multi-dimensional normal distribution; 4.6. Information contained in random variables; CHAPTER 5. FUNCTIONS OF RANDOM VARIABLES; 5.1. Moments of functions of random variables; 5.2. Distribution function of a function of a random variable; 5.3. Density of a function of a random variable; 5.4. Limit theorems; 5.5. Information contained in transformed random variables; CHAPTER 6. ESTIMATION OF PARAMETERS OF DISTRIBUTIONS.
- 6.1. Main problems of mathematical statistics6.2. Estimation of statistical characteristics; 6.3. Frequency as a probability estimate; 6.4. Estimation of the expectation and variance of a random variable; 6.5. Estimation of the expectation and covariance matrix of a random vector; 6.6. Testing hypotheses about parameters of distributions; CHAPTER 7. ESTIMATOR THEORY; 7.1. General properties of estimators; 7.2. Main methods for finding estimators; 7.3. Recursive estimation of the root of a regression equation; 7.4. Recursive estimation of the extremum point of a regression.
- CHAPTER 8. ESTIMATION OF DISTRIBUTIONS8.1. Estimators of densities and distribution functions; 8.2. Approximate representation of distributions; 8.3. Testing hypotheses about distributions; 8.4. Statistical simulation methods; CHAPTER 9. STATISTICAL MODELS, I; 9.1. Mathematical models; 9.2. Regression models; 9.3. Estimation of regressions; 9.4. Testing hypotheses about regressions; 9.5. Analysis of variance; CHAPTER 10. STATISTICAL MODELS, II; 10.1. Models described by difference equations; 10.2. Estimation of random variables determined by difference equations; 10.3. Factor models.