Theoretical Probability Distributions

A first Course in Probability Theory – Volume II

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241 pages
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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About the author

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 Co...


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