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Theoretical Probability Distributions

A first Course in Probability Theory – Volume II

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Language:  English
This is volume two of the book entitled “A First Course in Probability Theory”. It is primarily intended for undergraduate students of Statistics and mathematics.
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This is volume two of the book entitled “A First Course in Probability Theory”. It is primarily intended for undergraduate students of Statistics and mathematics. It can, however, be used by students of Social Sciences and mathematics-related courses.
This volume covers some theoretical probability distributions of discrete and continuous random variables, namely, Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Multinomial, Uniform, Exponential, Gamma, Beta and Normal Distributions. There are relationships among these theoretical distributions and such relationships are established.
The book has a large number of motivating solved examples and contains a lot of exercises at the end of each chapter.

  1. Preface To The First Edition
  2. Preface To The Second Edition
  3. Acknowledgement
  4. Greek Alphabets
  5. List Of Mathematical Notations And Conventions
  6. Bernoulli And Binomial Distributions
    1. Bernoulli Trial
    2. Bernoulli Distribution
    3. Binomial Distribution
    4. Exercises
  7. Geometric And Negative Binomial Distributions
    1. Geometric Distribution
    2. Negative Binomial Distribution
    3. Exercises
  8. Poisson, Hypergeometric And Multinomial Distributions
    1. Poisson Distribution
    2. Hypergeometric Distribution
    3. Multinomial Distribution
    4. Exercises
  9. Uniform, Exponential, Gamma And Beta Distributions
    1. Uniform Distribution
    2. Exponential Distribution
    3. Gamma Distribution
    4. Beta Distribution
    5. Exercises
  10. Normal Distribution I
    1. Introduction
    2. General Normal Distribution
    3. Standard Normal Distribution
    4. Standard Normal Tables
    5. Exercises
  11. Normal Distribution II
    1. Introduction 
    2. Calculation Of Standard Scores
    3. Calculating X Values For Given Probability
    4. Inverse Function Of Standard Normal Distribution
    5. Calculations Involving Deviations
    6. Relationship Between Normal And Other Distributions
    7. Exercises 
  12. Appendices
  13. A Statistical Tables
    1. Cumulative Binomial Distribution
    2. Cumulative Poisson Distribution
    3. Hypergeometric Distribution
    4. Standard Normal Distribution (Full Table)
    5. Standard Normal Distribution (Half Table) 
    6. Normal Density Function
  14. Summary Characteristics Of Special Distributions
    1. Special Discrete Probability Distributions
    2. Special Continuous Probability Distributions
  15. Relationships Among Special Probability Distributions
  16. Answers To Odd-Numbered Exercises 
  17. Bibliography

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.