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Summary Of The Book
An Introduction To Probability: Theory and Its Applications (Volume - 1) is exhaustive in content and in-depth in its approach, laying emphasis on both, theory and applications of probability. It has been designed as a textbook for students who want to grasp the basic conceptual knowledge of the probability theory and also apply it to practical problems.
The book opens with the first chapter introducing students to the Nature of Probability Theory, as well as providing a summarised account of its background and history. Thereafter, the rest of the sixteen chapters provide a study into many topics including, random variables, expectation, renewal theory, branching processes, random walk and ruin problems, recurrent events, compound distribution, Markov chains, and laws of large numbers.
The book is illustrated with practical examples to support and provide a better understanding of its theoretical concepts. An Introduction To Probability: Theory and Its Applications (Volume - 1) is a comprehensive textbook on probability that covers topics including the binomial and poisson distributions, the sample space, compound distributions, integral valued variables, and elements of combinatorial analysis, to name a few.
Furthermore, all the problems asked in the book have their solutions provided at the end of the book. Also, certain omissions and inclusions have been made, keeping in mind the current relevance of topics. For instance, probabilistic arguments has been done away with in order to include combinatorial artifices. Branching processes, the De Moivre-Laplace Theorem, and Markov Chain are other new additions to this book. The book also lists out which topics are meant purely for reading and can otherwise be omitted.
About William Feller
Considered one of the greatest Probabilists of the twentieth century, noted mathematician William Feller (Vilibald Sre?ko Feller) was of Croatian-American descent and born in 1906.
His writings in his books and papers pertain to subjects such as Theory of Measurement, Mathematical Analysis, Differential Equations, Functional Analysis, and Geometry.
Feller finished his schooling from his birthplace, Zagreb, and studied Maths for two years. Thereafter, he left for Germany where he continued his higher education, obtaining a doctorate in 1926. Initially, he took up teaching positions at the Universities of Kiel, Stockholm, and Lund, respectively. Eventually, he moved to the United States, gained citizenship there, and taught at Brown University, Cornell University, and Princeton University. Considered instrumental in his role in the inclusion of Probability Theory as a branch of Mathematical Analysis, he was the recipient of the distinguished National Medal Of Science in 1969. William Feller died in New York in January, 1970.
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TABLE OF CONTENTS
· Introduction: The Nature of Probability Theory
· The Sample Space
· Elements of Combinatorial Analysis
· Fluctuations in Coin Tossing and Random Walks
· Combination of Events
· Conditional Probability
· Stochastic Independence
· The Binomial and Poisson Distributions
· The Normal Approximation to the Binomial Distribution
· Unlimited Sequences of Bernoulli Trials
· Random Variables
· Laws of Large Numbers
· Integral Valued Variables
· Generating Functions
· Compound Distributions
· Branching Processes
· Recurrent Events
· Renewal Theory
· Random Walk and Ruin Problems
· Markov Chains
· Algebraic Treatment of Finite Markov Chains
· The Simplest Time-Dependent Stochastic Processes
· Answers to Problems