Unexpected expectancies: The Curiosities of a Mathematical Crystal Ball explores how paradoxical demanding situations concerning mathematical expectation frequently necessitate a reexamination of simple premises. the writer takes you thru mathematical paradoxes linked to probably simple functions of mathematical expectation and indicates how those unforeseen contradictions may possibly push you to reassess the legitimacy of the applications.

The booklet calls for merely an figuring out of uncomplicated algebraic operations and contains supplemental mathematical historical past in bankruptcy appendices. After a heritage of chance thought, it introduces the elemental legislation of likelihood in addition to the definition and purposes of mathematical expectation/expected worth (E). the rest of the textual content covers unforeseen effects concerning mathematical expectation, including:

• The roles of aversion and threat in rational choice making


• A category of anticipated price paradoxes often called envelope problems


• Parrondo’s paradox—how destructive (losing) expectancies will be mixed to offer a successful outcome


• Problems linked to imperfect recall


• Non-zero-sum video games, corresponding to the sport of chook and the prisoner’s dilemma


• Newcomb’s paradox—a nice philosophical paradox of unfastened will


• Benford’s legislation and its use in computing device layout and fraud detection

While worthy in components as various as online game idea, quantum mechanics, and forensic technology, mathematical expectation generates paradoxes that often depart questions unanswered but exhibit fascinating surprises. Encouraging you to include the mysteries of arithmetic, this ebook is helping you savour the functions of mathematical expectation, "a statistical crystal ball."

Listen to an interview with the writer on NewBooksinMath.com.