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The Pleasures of Probability

The Pleasures of Probability
Author: Richard Isaac
Publisher: Springer Science & Business Media
Total Pages: 249
Release: 2013-11-11
Genre: Mathematics
ISBN: 146120819X

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The ideas of probability are all around us. Lotteries, casino gambling, the al most non-stop polling which seems to mold public policy more and more these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairly decent mathematical background in elementary algebra to this world of probabil ity, to the way of thinking typical of probability, and the kinds of problems to which probability can be applied. I have used examples from a wide variety of fields to motivate the discussion of concepts.


The Pleasures of Statistics

The Pleasures of Statistics
Author: Frederick Mosteller
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2010-03-10
Genre: Mathematics
ISBN: 0387779566

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From his unique perspective, renowned statistician and educator Frederick Mosteller describes many of the projects and events in his long career. From humble beginnings in western Pennsylvania to becoming the founding chairman of Harvard University’s Department of Statistics and beyond, he inspired many statisticians, scientists, and students with his unabashed pragmatism, creative thinking, and zest for both learning and teaching. This candid account offers fresh insights into the qualities that made Mosteller a superb teacher, a prolific scholar, a respected leader, and a valued advisor. A special feature of the book is its chapter-length insider accounts of work on the pre-election polls of 1948, statistical aspects of the Kinsey report on sexual behavior in the human male, mathematical learning theory, authorship of the disputed Federalist papers, safety of anesthetics, and a wide-ranging examination of the Coleman report on equality of educational opportunity. This volume is a companion to Selected Papers of Frederick Mosteller (Springer, 2006) and A Statistical Model: Frederick Mosteller’s Contributions to Statistics, Science, and Public Policy (Springer-Verlag, 1990). Frederick Mosteller (1916–2006) was Roger I. Lee Professor of Mathematical Statistics at Harvard University. His manuscript was unfinished at his death and has been updated.


Introduction to Probability

Introduction to Probability
Author: David F. Anderson
Publisher: Cambridge University Press
Total Pages: 447
Release: 2017-11-02
Genre: Mathematics
ISBN: 110824498X

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This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.


The Pleasures of Counting

The Pleasures of Counting
Author: T. W. Körner
Publisher: Cambridge University Press
Total Pages: 548
Release: 1996-12-05
Genre: Mathematics
ISBN: 1316025454

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What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here.


Bayesian Statistics the Fun Way

Bayesian Statistics the Fun Way
Author: Will Kurt
Publisher: No Starch Press
Total Pages: 258
Release: 2019-07-09
Genre: Mathematics
ISBN: 1593279566

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Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples. Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that. This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples. By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to: - How to measure your own level of uncertainty in a conclusion or belief - Calculate Bayes theorem and understand what it's useful for - Find the posterior, likelihood, and prior to check the accuracy of your conclusions - Calculate distributions to see the range of your data - Compare hypotheses and draw reliable conclusions from them Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.


The Art of the Infinite

The Art of the Infinite
Author: Robert Kaplan
Publisher: Bloomsbury Publishing USA
Total Pages: 417
Release: 2014-02-04
Genre: Mathematics
ISBN: 1608198693

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Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.


Fifty Challenging Problems in Probability with Solutions

Fifty Challenging Problems in Probability with Solutions
Author: Frederick Mosteller
Publisher: Courier Corporation
Total Pages: 88
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486134962

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Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions.


Mathematical Statistics with Resampling and R

Mathematical Statistics with Resampling and R
Author: Laura M. Chihara
Publisher: John Wiley & Sons
Total Pages: 560
Release: 2018-09-17
Genre: Mathematics
ISBN: 1119416523

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This thoroughly updated second edition combines the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The second edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book has been classroom-tested to ensure an accessible presentation, uses the powerful and flexible computer language R for data analysis and explores the benefits of modern resampling techniques. This book offers an introduction to permutation tests and bootstrap methods that can serve to motivate classical inference methods. The book strikes a balance between theory, computing, and applications, and the new edition explores additional topics including consulting, paired t test, ANOVA and Google Interview Questions. Throughout the book, new and updated case studies are included representing a diverse range of subjects such as flight delays, birth weights of babies, and telephone company repair times. These illustrate the relevance of the real-world applications of the material. This new edition: • Puts the focus on statistical consulting that emphasizes giving a client an understanding of data and goes beyond typical expectations • Presents new material on topics such as the paired t test, Fisher's Exact Test and the EM algorithm • Offers a new section on "Google Interview Questions" that illustrates statistical thinking • Provides a new chapter on ANOVA • Contains more exercises and updated case studies, data sets, and R code Written for undergraduate students in a mathematical statistics course as well as practitioners and researchers, the second edition of Mathematical Statistics with Resampling and R presents a revised and updated guide for applying the most current resampling techniques to mathematical statistics.


Probability Theory

Probability Theory
Author:
Publisher: Allied Publishers
Total Pages: 436
Release: 2013
Genre:
ISBN: 9788177644517

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Probability theory


Proofs that Really Count

Proofs that Really Count
Author: Arthur T. Benjamin
Publisher: American Mathematical Society
Total Pages: 210
Release: 2022-09-21
Genre: Mathematics
ISBN: 1470472597

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Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.