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A First Look at Rigorous Probability Theory
This textbook is an introduction to rigorous probability theory using measure theory. It provides rigorous, complete proofs of all the essential introductory mathematical results of probability theory and measure theory. More advanced or specialized areas are entirely omitted or only hinted at. For example, the text includes a complete proof of the classical central limit theorem, including the necessary continuity theorem for characteristic functions, but the more general Lindeberg central limit theorem is only outlined and is not proved. Similarly, all necessary facts from measure theory are proved before they are used, but more abstract or advanced measure theory results are not included. Furthermore, measure theory is discussed as much as possible purely in terms of probability, as opposed to being treated as a separate subject which must be mastered before probability theory can be understood.
A First Look at Rigorous Probability Theory
Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.
Struck By Lightning
Human beings have long been both fascinated and appalled by randomness. On the one hand, we love the thrill of a surprise party or the freedom of not knowing what tomorrow will bring. We are inexplicably delighted by strange coincidences and striking similarities. But we also hate uncertainty's dark side. From cancer to bird flu, diseases may strike with no apparent pattern. Terrorists attack, airplanes crash, bridges collapse, and we never know if we'll be that one-in-a-million statistic. In this entertaining look at the world of probabilities, Jeffrey Rosenthal, maths professor and improvisational comedian, explains the mechanics of randomness in fields as diverse as poker hands, email spam, crime statistics, opinion polls and lottery jackpots. Read Struck by Lightning and, chances are, you will never look at the world the same way again.
Struck by Lightning
From lotteries, opinion polls and insuranceto worries about murder rates, naturaldisasters and terrorism, probability plays amajor part in our everyday lives--a partthat is frequently and needlessly misunderstood.Jeffrey S. Rosenthal, a mathprofessor and improvisational comedian,comes to the rescue with this irreverent,bestselling exploration of the odds andoddities of randomness. Looking at suchfamiliar topics as poker hands, e-mailspam, political elections and game shows,Struck by Lightning puts probability intoperspective and has fun along the way.
Knock on Wood
Jeffrey S. Rosenthal, author of the bestseller Struck by Lightning: The Curious World of Probabilities, was born on Friday the thirteenth, a fact that he discovered long after he had become one of the world’s pre-eminent statisticians. Had he been living ignorantly and innocently under an unlucky cloud for all those years? Or is thirteen just another number? As a scientist and a man of reason, Rosenthal has long considered the value of luck, good and bad, seeking to measure chance and hope in formulas scratched out on chalkboards. In Knock on Wood, with great humour and irreverence, Rosenthal divines the world of luck, fate and chance, putting his considerable scientific acumen to the test in deducing whether luck is real or the mere stuff of superstition.
Probability and Statistics
Unlike some more traditional introductory mathematics and statistics competitors, Probability and Statistics: The Science of Uncertainty brings a modern flavour to the course, incorporating the computer and offering an integrated approach to inference that includes the frequency approach and the Bayesian inference. From the start of the book, it integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout. Maths and science students (both undergraduate and postgraduate) with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. The second edition now includes a number of features designed to make the material more accessible and level-appropriate to the students taking this course today.
The Curious World Of Probabilities
From lotteries, opinion polls and insurance policies to worries about murder rates, natural disasters and terrorism, probability plays a major part in our everyday lives a part that is frequently and needlessly misunderstood. Jeffrey S. Rosenthal, a math professor and improvisational comedian, comes to the rescue with this irreverent, bestselling exploration of the odds and oddities of randomness. Looking at such familiar topics as poker hands, e-mail spam, elections and game shows, The Curious World Of Probabilities elucidates and entertains. Chances are, you will never look at the world in the same way again.
A First Look at Stochastic Processes
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory. Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms. The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
