probability-theory-an-elementary-course

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Probability Theory

Author : 林正炎
ISBN : 7308198790
Genre : Probabilities
File Size : 75. 10 MB
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Advanced Probability Theory Second Edition

Author : Janos Galambos
ISBN : 0824793323
Genre : Mathematics
File Size : 64. 48 MB
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This work thoroughly covers the concepts and main results of probability theory, from its fundamental principles to advanced applications. This edition provides examples early in the text of practical problems such as the safety of a piece of engineering equipment or the inevitability of wrong conclusions in seemingly accurate medical tests for AIDS and cancer.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

Probability Theory And Applications

Author : Enders A. Robinson
ISBN : 9789400953864
Genre : Mathematics
File Size : 66. 98 MB
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Probability theory and its applications represent a discipline of fun damental importance to nearly all people working in the high-tech nology world that surrounds us. There is increasing awareness that we should ask not "Is it so?" but rather "What is the probability that it is so?" As a result, most colleges and universities require a course in mathematical probability to be given as part of the undergraduate training of all scientists, engineers, and mathematicians. This book is a text for a first course in the mathematical theory of probability for undergraduate students who have the prerequisite of at least two, and better three, semesters of calculus. In particular, the student must have a good working knowledge of power series expan sions and integration. Moreover, it would be helpful if the student has had some previous exposure to elementary probability theory, either in an elementary statistics course or a finite mathematics course in high school or college. If these prerequisites are met, then a good part of the material in this book can be covered in a semester (IS-week) course that meets three hours a week.

A Course On Elementary Probability Theory

Author : Aladji Babacar Niang
ISBN : 9798582099772
Genre :
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This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability theory. The theory is preceded by a general chapter on counting methods. Then, the theory of probabilities is presented in a discrete framework. Two objectives are sought. The first is to give the reader the ability to solve a large number of problems related to probability theory, including application problems in a variety of disciplines. The second is to prepare the reader before he takes course on the mathematical foundations of probability theory. In this later book, the reader will concentrate more on mathematical concepts, while in the present text, experimental frameworks are mostly found. If both objectives are met, the reader will have already acquired a definitive experience in problem-solving ability with the tools of probability theory and at the same time he is ready to move on to a theoretical course on probability theory based on the theory of Measure and Integration. The book ends with a chapter that allows the reader to begin an intermediate course in mathematical statistics.

Probability Theory

Author : L. E. Maistrov
ISBN : 9781483218632
Genre : Mathematics
File Size : 32. 15 MB
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Probability Theory: A Historical Sketch covers the probability theory, mainly axiomatization problems. The book discusses the prehistory of the probability theory; the first stage in the development of probability theory; and the development of probability theory to the middle of the 19th century. The text also describes the probability theory in the second half of the 19th century; and the axiomatic foundations of the probability theory. Historians and mathematicians will find the book invaluable.

Modern Probability Theory

Author : B. Ramdas Bhat
ISBN : 8122411894
Genre : Probabilities
File Size : 82. 67 MB
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The Book Continues To Cover The Syllabus Of A One-Year Course On Probability Theory. The Rigorous Axiomatic Approach Continues To Be Followed. For Those Who Plan To Apply Probability Models In Their Chosen Areas The Book Will Provide The Necessary Foundation. For Those Who Want To Proceed To Work In The Area Of Stochastic Processes, The Present Work Will Provide The Necessary Preliminary Background. It Can Be Used By Probabilists, Statisticians And Mathematicians. In The Present Revised Edition Many Concepts Have Been Elaborated. Clarifications Are Given For A Number Of Steps In The Proofs Of Results Derived. Additional Examples And Problems Are Given At The End Of Different Chapters. An Additional Preliminary Chapter Has Been Added So That Students Can Recapitulate The Topics Normally Covered In The Undergraduate Courses. It Also Forms The Foundation For Topics Covered In The Remaining Chapters. The Third Edition Incorporates The Suggestions For Improvements Received By The Author When The Earlier Editions Were In Circulation. With The Additional Features And Most Of The Errors Weeded Out, The Book Is Hoped To Become More Useful In The Hands Of Students And Teachers.

Essentials Of Probability Theory For Statisticians

Author : Michael A. Proschan
ISBN : 9781498704229
Genre : Mathematics
File Size : 44. 47 MB
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Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.

Probability With A View Towards Statistics

Author : J. Hoffman-Jorgensen
ISBN : 0412052210
Genre : Mathematics
File Size : 83. 1 MB
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Volume I of this two-volume text and reference work begins by providing a foundation in measure and integration theory. It then offers a systematic introduction to probability theory, and in particular, those parts that are used in statistics. This volume discusses the law of large numbers for independent and non-independent random variables, transforms, special distributions, convergence in law, the central limit theorem for normal and infinitely divisible laws, conditional expectations and martingales. Unusual topics include the uniqueness and convergence theorem for general transforms with characteristic functions, Laplace transforms, moment transforms and generating functions as special examples. The text contains substantive applications, e.g., epidemic models, the ballot problem, stock market models and water reservoir models, and discussion of the historical background. The exercise sets contain a variety of problems ranging from simple exercises to extensions of the theory.

Probability With A View Towards Statistics Volume I

Author : J. Hoffman-Jorgensen
ISBN : 9781351421584
Genre : Mathematics
File Size : 90. 59 MB
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Volume I of this two-volume text and reference work begins by providing a foundation in measure and integration theory. It then offers a systematic introduction to probability theory, and in particular, those parts that are used in statistics. This volume discusses the law of large numbers for independent and non-independent random variables, transforms, special distributions, convergence in law, the central limit theorem for normal and infinitely divisible laws, conditional expectations and martingales. Unusual topics include the uniqueness and convergence theorem for general transforms with characteristic functions, Laplace transforms, moment transforms and generating functions as special examples. The text contains substantive applications, e.g., epidemic models, the ballot problem, stock market models and water reservoir models, and discussion of the historical background. The exercise sets contain a variety of problems ranging from simple exercises to extensions of the theory.

Probability Theory An Elementary Course

Author : Zhengyan Lin
ISBN : 981120019X
Genre :
File Size : 33. 86 MB
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Probability theory is a discipline that studies the quantitative regularity of random phenomena. The fact that random phenomena arise, especially in the era of big data and artificial intelligence, determines the importance of this discipline. This volume introduces various concepts that quantitatively describe random phenomena, including probability, random variables, distribution functions, density functions, mathematical expectations, variance, moments, and characteristic functions. It finishes off by presenting probability limit theory, including various convergences.Throughout the volume, great importance is attached to the elaboration of probability thoughts. For this reason, some practical examples to illustrate the introduced concept are always used. In order to meet the needs of different levels of readers, there is a section on Supplements and Notes at the end of each chapter to enhance and expand the content in the body of the textbook. This volume contains a large number of problems of varying levels for the reader with the purpose to review, consolidate, deepen and expand their knowledge.As the only branch of mathematics that studies the quantitative regularity of random phenomena, probability theory has not only theoretical significance, but it is also a main theoretical basis of mathematical statistics. Therefore, it will be of interest to scholars from other disciplines related to random phenomena.

Elementary Probability Theory

Author : Melvin Hausner
ISBN : 9781461517535
Genre : Mathematics
File Size : 83. 36 MB
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This text contains ample material for a one term precalculus introduction to probability theory. lt can be used by itself as an elementary introduc tion to probability, or as the probability half of a one-year probability statistics course. Although the development of the subject is rigorous, experimental motivation is maintained throughout the text. Also, statistical and practical applications are given throughout. The core of the text consists of the unstarred sections, most of chapters 1-3 and 5-7. Included are finite probability spaces, com binatorics, set theory, independence and conditional probability, random variables, Chebyshev's theorem, the law of large numbers, the binomial distribution, the normal distribution and the normal approxi mation to the binomial distribution. The starred sections include limiting and infinite processes, a mathematical discussion of symmetry, and game theory. These sections are indicated with an*, and are optional and sometimes more difficult. I have, in most places throughout the text, given decimal equivalents to fractional answers. Thus, while the mathematician finds the answer p = 17/143 satisfactory, the scientist is best appeased by the decimal approximation p = 0.119. A decimal answer gives a ready way of find ing the correct order of magnitude and of comparing probabilities.

Probability Theory

Author : Yakov G. Sinai
ISBN : 9783662028452
Genre : Mathematics
File Size : 66. 46 MB
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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. The first part of the book covers discrete random variables, using the same approach, basedon Kolmogorov's axioms for probability, used later for the general case. The text is divided into sixteen lectures, each covering a major topic. The introductory notions and classical results are included, of course: random variables, the central limit theorem, the law of large numbers, conditional probability, random walks, etc. Sinai's style is accessible and clear, with interesting examples to accompany new ideas. Besides statistical mechanics, other interesting, less common topics found in the book are: percolation, the concept of stability in the central limit theorem and the study of probability of large deviations. Little more than a standard undergraduate course in analysis is assumed of the reader. Notions from measure theory and Lebesgue integration are introduced in the second half of the text. The book is suitable for second or third year students in mathematics, physics or other natural sciences. It could also be usedby more advanced readers who want to learn the mathematics of probability theory and some of its applications in statistical physics.

Invited Lectures From The 13th International Congress On Mathematical Education

Author : Gabriele Kaiser
ISBN : 9783319721705
Genre : Education
File Size : 70. 27 MB
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The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Elementary Stochastic Calculus With Finance In View

Author : Thomas Mikosch
ISBN : 9789813105294
Genre : Mathematics
File Size : 54. 62 MB
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Modelling with the Itô integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Itô calculus and/or stochastic finance.

Canadian Mathematical Bulletin

Author :
ISBN :
Genre :
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Introduction To The Theory Of Non Symmetric Dirichlet Forms

Author : Zhi-Ming Ma
ISBN : 9783642777394
Genre : Mathematics
File Size : 68. 30 MB
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The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is based on recent joint work of S. Albeverio and the two authors and on a one-year-course on Dirichlet forms taught by the second named author at the University of Bonn in 1990/9l. It addresses both researchers and graduate students who require a quick but complete introduction to the theory. Prerequisites are a basic course in probabil ity theory (including elementary martingale theory up to the optional sampling theorem) and a sound knowledge of measure theory (as, for example, to be found in Part I of H. Bauer [B 78]). Furthermore, an elementary course on lin ear operators on Banach and Hilbert spaces (but without spectral theory) and a course on Markov processes would be helpful though most of the material needed is included here.

The Random Walks Of George Polya

Author : Gerald L. Alexanderson
ISBN : 0883855283
Genre : Mathematics
File Size : 73. 39 MB
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Both a biography of Plya's life, and a review of his many mathematical achievements by today's experts.

Probability Theory

Author : Y. A. Rozanov
ISBN : 9780486321141
Genre : Mathematics
File Size : 77. 20 MB
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This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.

University Of Michigan Official Publication

Author :
ISBN : UOM:39015078932822
Genre : Education, Higher
File Size : 89. 31 MB
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Ross

Author : SHELDON. ROSS
ISBN : 1292269200
Genre :
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This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States. For upper-level to graduate courses in Probability or Probability and Statistics, for majors in mathematics, statistics, engineering, and the sciences. Explores both the mathematics and the many potential applications of probability theory A First Course in Probability offers an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explanations, it attempts to present not only the mathematics of probability theory, but also the many diverse possible applications of this subject through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for inherent interest and for use in building student intuition about probability.

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