Unexpected Expectations The Curiosities of a Mathematical Crystal Ball
Auteur : Wapner Leonard M.
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."
The Crystal Ball. Looking Back. The ABCs of E. Doing the Right Thing. Aversion Perversion. And the Envelope Please! Parrondo’s Paradox: You Can Win for Losing. Imperfect Recall. Non-Zero-Sum Games: The Inadequacy of Individual Rationality. Newcomb’s Threat. Benford’s Law. Let the Mystery Be! Bibliography. Index.
Date de parution : 12-2019
15.2x22.9 cm
Disponible chez l'éditeur (délai d'approvisionnement : 12 jours).
Prix indicatif 77,90 €
Ajouter au panierDate de parution : 07-2012
Ouvrage de 200 p.
15.2x22.9 cm
Thèmes d’Unexpected Expectations :
Mots-clés :
Benford’s Law; Newcomb’s Paradox; benford's; Mathematical Expectation; law; Theoretical Relative Frequency; mathematical; Row Player; newcomb's; Benford Distribution; paradox; Column Player; theoretical; Prisoner’s Dilemma; relative; James Stein Estimators; frequency; Television Game Show; prisoners; Coin Toss; dilemma; Nonzero Sum Game; Imperfect Recall; True Probability; Envelope Problem; Non-zero Sum Games; Preplay Communication; Game 2A; Game 2B; Newcomb’s Problem; Leading Digit; Small SSE; Monty Hall Problem; Ludo Aleae; Dictator Game