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# Advanced Topics In Introductory Probability

### A first Course in Probability Theory – Volume III

275
Language:  English
This textbook contains the extension of univariate random variable to multivariate random variables with emphasis on Bivariate Distributions.
Содержание
Описание
1. Chapter 1 Probability And Distribution Functions of Bivariate Distributions
1. Introduction
2. Concept of Bivariate Random Variables
3. Joint Probability Distributions
4. Joint Cumulative Distribution Functions
5. Marginal Distribution of Bivariate Random Variables
6. Conditional Distribution of Bivariate Random Variables
7. Independence of Bivariate Random Variables
2. Chapter 2 Sums, Differences, Products and Quotients of Bivariate Distributions
1. Introduction
2. Sums of Bivariate Random Variables
3. Differences of Random Variables
4. Products of Bivariate Random Variables
5. Quotients of Bivariate Random Variables
3. Chapter 3 Expectation and Variance of Bivariate Distributions
1. Introduction
2. Expectation of Bivariate Random Variables
3. Variance of Bivariate Random Variables
4. Chapter 4 Measures of Relationship of Bivariate Distributions
1. Introduction
2. Product Moment
3. Covariance of Random Variables
4. Correlation Coefficient of Random Variables
5. Conditional Expectations
6. Conditional Variances
7. Regression Curves
5. Chapter 5 Statistical Inequalities and Limit Laws
1. Introduction
2. Markov’s Inequality
3. Chebyshev’s Inequality
4. Law of Large Numbers
5. Central Limit Theorem
6. Chapter 6 Sampling Distributions I: Basic Concepts
1. Introduction
2. Statistical Inference
3. Probability Sampling
4. Sampling With and Without Replacement
7. Chapter 7 Sampling Distributions II: Sampling Distribution of Statistics
1. Introduction
2. Sampling Distribution of Means
3. Sampling Distribution of Proportions
4. Sampling Distribution of Differences
5. Sampling Distribution of Variance
8. Chapter 8 Distributions Derived from Normal Distribution
1. Introduction
2. χ2 Distribution
3. t Distribution
4. F Distribution
9. Statistical Tables