Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these

Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball explores how paradoxical challenges involving mathematical expectation often necessitate a reexamination of basic premises. The author takes you through mathematical paradoxes associated with seemingly straightforward applications of mathematical expectation and shows how these unexpected contradictions may push you to reconsider the legitimacy of the applications. The book requires only an understanding of basic algebraic operations and includes supplemental mathematical background in chapter appendices. After a history of probability theory, it introduces the basic laws of probability as well as the definition and applications of mathematical expectation/expected value (E). The remainder of the text covers unexpected results related to mathematical expectation, including: The roles of aversion and risk in rational decision making A class of expected value paradoxes referred to as envelope problems Parrondo’s paradox—how negative (losing) expectations can be combined to give a winning result Problems associated with imperfect recall Non-zero-sum games, such as the game of chicken and the prisoner’s dilemma Newcomb’s paradox—a great philosophical paradox of free will Benford’s law and its use in computer design and fraud detection While useful in areas as diverse as game theory, quantum mechanics, and forensic science, mathematical expectation generates paradoxes that frequently leave questions unanswered yet reveal interesting surprises. Encouraging you to embrace the mysteries of mathematics, this book helps you appreciate the applications of mathematical expectation, "a statistical crystal ball." Listen to an interview with the author on NewBooksinMath.com.

KevinWith everyone around me settling down, I'm happy to continue living my life single and carefree. That is unless I can convince the concierge, Lucy Wilson at 425 Madison to finally take me up on that offer to go out on a date.She's beautiful, friendly, and her compassion for each and every one of the residents is admirable. Something tells me that she doesn't see herself that way at all though. This is why I've made it my mission to break her out of her overly cautious shell starting with a lucky penny and a $10 raffle ticket.It was all supposed to be a little fun but when a large dose of lucky graces us, everything suddenly becomes unexpected.LucyHe thinks I don't see him, but I do. Oh yes, I've been aware of the all too good looking Kevin Harper for quite some time now. The thing is, I'm not sure that we have enough in common and I sure don't have the free time for a social life between my job and school. Dating? That's pretty far down on the list of things I'd like to check off - not by choice. That is until Kevin convinces me that a little fun is good for the soul. What started as a $10 raffle ticket turned into a vacation in Vegas and a whole lot of expectations that neither of us saw coming.I always believed in fairy tales, but I wonder if what we have is too good to be true. I can only hope that it's true what they say...After all, 425 Madison is the perfect place to fall in love.

Duane Elmer offers the tools needed to reduce apprehension, communicate effectively and establish genuine trust and acceptance between cultures while demonstrating how we can avoid being cultural imperialists and instead become authentic ambassadors for Christ.

The book shows how to use Planning by Design (PxD) for developing working models to any type of subject area. Section 1 describes the nature of planning in general, the formula of planning, the features that make it systematic, the essence of PxD, and developing and using the working model. Section 2 demonstrates personal application of creative planning to real life cases and practical working models on different subject areas. The book provides a general planning "master guide" that shows how to develop a working model of any definable subject matter. This objective will be accomplished by introducing the concepts, the process, and the methodology of PxD.

Socrates used facilitative methods in teaching philosophy, and for good reason: They work! Fast forward to today, and managers, supervisors, consultants, trainers, and others are learning to use facilitative techniques to improve performance in the workplace and other areas that demand results. The authors of this series, led by an expert with twenty-five years of experience as a professional facilitator, provide a complete model of group facilitation in Process-Based Facilitation. In this first volume, they introduce the basic skills of facilitation, the process-based facilitation model, many facilitation methods, and evaluation of the facilitators methods and assessment of style. Inside, youll get: ? tested and proven facilitation planning methods, including dozens of worksheets; ? explanations on elements of the process-based facilitation model; ? Discussion reviews the seven values of facilitation and twelve core principles of facilitation; ? multiple methods to guide intervention as a facilitator; ? sixty-five articles describing concept models, frameworks, tools, and techniques of facilitation. Loaded with figures, tables, and worksheets, this book is easy to read, review, and most importantuse. Whether youre a novice or a professional, this book will help you apply facilitative techniques to succeed in and out of work.

Can we correctly predict the flip of a fair coin more than half the time — or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50-50 guesses.But mathematics is filled with counterintuitive results — and this book discusses some surprising and entertaining examples. It is possible to devise experiments in which a flipped coin lands heads completely at random half the time, but we can also correctly predict when it will land heads more than half the time. The Fate of Schrodinger's Cat shows how high-school algebra and basic probability theory, with the invaluable assistance of computer simulations, can be used to investigate both the intuitive and the counterintuitive.This book explores fascinating and controversial questions involving prediction, decision-making, and statistical analysis in a number of diverse areas, ranging from whether there is such a thing as a 'hot hand' in shooting a basketball, to how we can successfully predict, more than half the time, the decay of the radioactive atom that determines the fate of Schrodinger's Cat.