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Introductory Probability Theory

A first Course in Probability Theory – Volume I

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Language:  English
This book covers the basic theory of probability in a simple yet easily comprehensible manner. It deals with the basic mathematical tools for the understanding of probability.
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  1. Set Theory 
    1. Introduction 
    2. Sets 
    3. Set Operations 
    4. Classes Of Sets 
    5. Laws Of Algebra Of Sets 
    6. Venn Diagrams 
  2. Counting principles 
    1. Introduction 
    2. Sampling with or without replacement 
    3. Addition and multiplication principles of counting 
    4. Permutations: ordered selection 
    5. Combinations: unordered selection 
    6. Binomial theorem 
    7. Multinomial theorem 
  3. Basic concepts in probability 
    1. Introduction 
    2. Experiments 
    3. Sample spaces 
    4. Events 
    5. Concept of probability 
  4. Basic probability laws and theorems 
    1. Introduction 
    2. Addition law of probability 
    3. Law of complementation 
    4. Inequality of probabilities 
    5. Conditional probability 
    6. Multiplication law of probability 
    7. Total probability law 
    8. Bayes’ theorem 
    9. Statistical independence 
  5. Random variables 
    1. Introduction 
    2. Concept of random variable 
    3. Probability distribution of random variable 
    4. Cumulative distribution function 
    5. Conditional probability of random variable 
  6. Numerical characteristics of random variables 
    1. Introduction 
    2. Measures of location 
    3. Mode 
    4. Median 
    5. Quantiles 
    6. Mathematical expectation 
    7. Variance 
  7. Moments and moment-generating functions 
    1. Introduction 
    2. Types of moments 
    3. Uses of moments 
    4. Moment-generating functions 

Introductory Probability Theory is volume one of the book entitles “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 the basic theory of probability in a simple yet easily comprehensible manner. It deals with the basic mathematical tools for the understanding of probability, such as, the set theory and the counting principles, the concept of probability, basic probability calculus, laws and theorems, the random variable, its probability distribution and numerical characterization. Determination of central and non-central location of distributions as well as their spread are extensively discussed. Moments and moment-generating functions have also been extensively covered. 

The book has a large number of motivating solved examples. It has a large number of exercises at the end of each chapter for students’ practice.

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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.