Advanced Topics In Introductory Probability

Content

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 
   
10. Answers to Odd-Numbered Exercises 
    
11. Bibliography 
    

Description

This is the final book in a series of textbooks on first course in Probability Theory. The first book is on the basic probability theory, random variables and probability distributions. The second volume is on theoretical distributions, including Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Multinomial, Uniform, Exponential, Gamma, Beta and Normal Distributions.
This textbook contains the extension of univariate random variable to multivariate random variables with emphasis on Bivariate Distributions. It also covers topics on Statistical Inequalities, Limit Laws, Sampling Distributions as well as Chi square, t and F Distributions.
The book has a large number of motivating solved examples and also contains a lot of exercises at the end of each chapter.