At one level, this book surveys recent findings about the existence of planets orbiting other sun-like stars, such as 51 Pegasi (discovered in 1995) and Tau Bootis. It addresses questions such as what life is and what intelligent life is, as well as theories about how life evolved on Earth from basic molecules into more complex organic compounds leading to DNA. The existence of similar molecules on other planets in our solar system, as well as in meteorites that land on Earth every year, is used in an argument for the evolution of such compounds - the building blocks of life - outside Earth. At the same time, the author applies the laws of large numbers to the immense size of the known universe, with its billions of galaxies, each containing many billions of stars, to argue the probability that there is life elsewhere.

Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks and the Kalman-Bucy filter. Examples are discussed in detail, and there are a large number of exercises. This third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.

Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Probability theory

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Designed for the intellectually curious, this book provides a solid foundation in basic probability theory in a charming style, without technical jargon. This text will immerse the reader in a mathematical view of the world, and teach them techniques to solve real-world problems both inside and outside the casino.