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Advanced Topics In Introductory Probability

A first Course in Probability Theory – Volume III

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Language:  English
This textbook contains the extension of univariate random variable to multivariate random variables with emphasis on Bivariate Distributions.
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  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 

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.

About the Author

Nicholas N.N. Nsowah-Nuamah

Professor Nicholas N. N. Nsowah–Nuamah, a full Professor of Statistics at the Institute of Statistical Social and Economic Research (ISSER), University of Ghana, is currently the President of Dominion University College in Ghana.

Until then, he was the President of Regent University College of Science and Technology, the foundation Interim Vice Chancellor of Kumasi Technical University and the last Rector of Kumasi Polytechnic. He was the Deputy and also the Acting Government Statistician at the Ghana Statistical Service. He is the President of the Ghana Statistical Association.

At ISSER, he was the Head of Statistics, Computing, Communication and Information Division and also Coordinator of the Certificate and Diploma programmes in Statistics. He has taught Statistics at various levels: Diploma, degree and postgraduate. He has published widely and written more than 18 books in different areas of Statistics. Among them are: Regression Analysis: Theory, Methods, Analysis and Interpretation, A First Course in Probability Theory, VoI-Vol III, Introduction to Probability and Stochastic Processes, Demographic Statistics: A Handbook of Methods and Measures in Demography, Analysis of Variance: Analytical Technique for Experimental Designs, Intermediate Design and Analysis of Experiments, Missing Observations and Incomplete Data in Experimental Designs, Advanced Design and Analysis of Experiments, Basic Statistics: A Handbook of Descriptive Statistics for Social and Biological Sciences, and Statistics for Health Schools and Professionals.