While the typesetting was done by myself, the images were produced by Mr Joshua Appiah, a former staff of mine at Kumasi Technical University, where I was their Interim Vice Chancellor. Volume I deals with probability calculus and probability distributions and Volume II treats special topics in probability theory. Much of the recent literature in probability appears to be inaccessible to many students, in large part, I believe, because rigour has taken precedence over the communication of fundamental ideas.
Some students had bitter experiences in schools with the teaching of probability and are already scared before starting the undergraduate course.
The problem is compounded when the student realises that many available textbooks do not treat the topics in a friendly way. In view of this the rigour of other books has been avoided. I have also tried very hard to use notation that is at once consistent and intuitive. The only mathematical prerequisite in this Volume is a knowledge of elementary course in Calculus. An exposure to differentiation, integration, series and some ideas of convergence should be sufficient. Within the chapters, important concepts are set out as definitions enclosed in double boxes while the main theoretical results of concepts and meanings are set out as theorems enclosed in single boxes.
Results which follow almost immediately from theorems with very little additional argument are stated as corollaries. Proofs have been provided to almost all theorems and corollaries stated. We implore the reader to clearly understand the definitions and implications of the theorems and corollaries although it is not always necessary to understand the proof of each theorem.
Many instructors and students will prefer to skim through these proofs, especially in a first course, although we hope that most will choose not to omit them completely. The notes, a common feature of the book, are an important part in three respects. Firstly, they illuminate points made in the text. Secondly, they present material that does not quite fit anywhere else and thirdly, they discuss details whose exposition would disturb the flow of the argument. In this Volume more than worked examples have been provided and it is essential that the student goes through all of them.
Probability theory requires a lot of practice from the student. I have therefore provided a set of questions at the end of each chapter. These exercises, which are more than , form an integral part of the text and it is essential that the student goes through many of them. Besides, the ability of students to grasp probability theory may be diverse from year to year.
In view of this, there is purposely more material here than may be required. Now a brief tour through this Volume. In Chapter 1 a brief account of Set Theory is given.
Chapter 2 describes a number of counting tricks that are very useful in solving probability problems. These first two chapters do not really discuss probability at all.
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Instead, they present the essential mathematical tools that are needed in the rest of the book. Although you may have dealt with these concepts in high school, it is important that these two chapters be utilised at least by the independent reader to assure a sound base for the applications in probability. Together with this, a detailed treatment of basic concepts in probability theory, such as experiments, sample spaces, and events in Chapter 3 make the book self-contained both as a reference and a text.
Statistics and probability
The materials in Chapters 4—12 form the heart of any introductory course in probability theory. Chapters 4, 5 and 6 give the basic theory of probability while Chapters 7 to 12 treat special probability distributions.
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We shall go through the basic content of Volume II. Chapters 1—4 extend the concept of a univariate random variable to multivariate random variables, even though emphasis is on Bivariate Distributions. Chapter 3 treats Expectation and Variance of Random Variables and their properties. Chapter 4 discusses various forms of Moments of bivariate distributions, and goes on to discuss Covariance, Correlation, Conditional Expectations and Regression Curves. It is possible that a book as detailed and technical as this one may not be free from errors.
If there are few errors it was because l had the assistance of a great many people in reading the preliminary drafts. R and the Department of Statistics all of the University of Ghana, in this respect. They pointed out a disconcertingly large number of mistakes, mostly typographical in nature. I thank Nathaniel Kwawukume for the many hours he devoted to going through most of the chapters and the extremely valuable suggestions he made.
I am also indebted to Dr. Atsem of Department of Statistics, University of Ghana, who critically read through the final draft and made very useful suggestions. I owe special thanks to two anonymous reviewers who spent substantial time reviewing the manuscript and who provided numerous helpful comments. The book is suitable for second or third year students in mathematics, physics or other natural sciences.
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About this Textbook Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners. Show all.
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