Nguồn ngoài
Applied Probability
This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation.
- Tác giả
- Paul Pfeiffer
- Nhà xuất bản
- Rice University
- Nguồn
- LibreTexts
- Giấy phép
- CC BY
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 74 mục
- 01: Probability Systems
- 1.01: Likelihood
- 1.02: Probability Systems
- 1.03: Interpretations
- 1.04: Problems on Probability Systems
- 02: Minterm Analysis
- 2.01: Minterms
- 2.02: Minterms and MATLAB Calculations
- 2.03: Problems on Minterm Analysis
- 03: Conditional Probability
- 3.01: Conditional Probability
- 3.02: Problems on Conditional Probability
- 04: Independence of Events
- 4.01: Independence of Events
- 4.02: MATLAB and Independent Classes
- 4.03: Composite Trials
- 4.04: Problems on Independence of Events
- 05: Conditional Independence
- 5.01: Conditional Independence
- 5.02: Patterns of Probable Inference
- 5.03: Problems on Conditional Independence
- 06: Random Variables and Probabilities
- 6.01: Random Variables and Probabilities
- 6.02: Problems on Random Variables and Probabilities
- 07: Distribution and Density Functions
- 7.01: Distribution and Density Functions
- 7.02: Distribution Approximations
- 7.03: Problems on Distribution and Density Functions
- 08: Random Vectors and Joint Distributions
- 8.01: Random Vectors and Joint Distributions
- 8.02: Random Vectors and MATLAB
- 8.03: Problems on Random Vectors and Joint Distributions
- 09: Independent Classes of Random Variables
- 9.01: Independent Classes of Random Variables
- 9.02: Problems on Independent Classes of Random Variables
- 10: Functions of Random Variables
- 10.01: Functions of a Random Variable
- 10.02: Function of Random Vectors
- 10.03: The Quantile Function
- 10.04: Problems on Functions of Random Variables
- 11: Mathematical Expectation
- 11.01: Mathematical Expectation- Simple Random Variables
- 11.02: Mathematical Expectation and General Random Variables
- 11.03: Problems on Mathematical Expectation
- 12: Variance Covariance and Linear Regression
- 12.01: Variance
- 12.02: Covariance and the Correlation Coefficient
- 12.03: Linear Regression
- 12.04: Problems on Variance Covariance Linear Regression
- 13: Transform Methods
- 13.01: Transform Methods
- 13.02: Convergence and the Central Limit Theorem
- 13.03: Simple Random Samples and Statistics
- 13.04: Problems on Transform Methods
- 14: Conditional Expectation Regression
- 14.01: Conditional Expectation Regression
- 14.02: Problems on Conditional Expectation Regression
- 15: Random Selection
- 15.01: Random Selection
- 15.02: Some Random Selection Problems
- 15.03: Problems on Random Selection
- 16: Conditional Independence Given a Random Vector
- 16.01: Conditional Independence Given a Random Vector
- 16.02: Elements of Markov Sequences
- 16.03: Problems on Conditional Independence Given a Random Vector
- 17: Appendices
- 17.01: Appendix A to Applied Probability- Directory of m-functions and m-procedures
- 17.02: Appendix B to Applied Probability- some mathematical aids
- 17.03: Appendix C- Data on some common distributions
- 17.04: Appendix D to Applied Probability- The standard normal distribution
- 17.05: Appendix E to Applied Probability - Properties of Mathematical Expectation
- 17.06: Appendix F to Applied Probability- Properties of conditional expectation given a random vector
- 17.07: Appendix G to Applied Probability- Properties of conditional independence given a random vector
- 17.08: Matlab files for Problems in Applied Probability