Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 13)

This set of solved problems involves measure theory and probability and the level of difficulty is that of the Ph. D. student. The problems delve deeply into the theory of probability, independence, Gaussian variables, distributed computations and random processes. There are approximately 100 problems and nearly complete solutions to all of them are included. There is a statement on the back cover that many of the problems can lead the student on to research topics in probability and I fully agree with that. The chapter headings are: \*) Measure theory and probability \*) Independence and conditioning \*) Gaussian variables \*) Distributional computations \*) Convergence of random variables \*) Random processes This is an excellent self-study guide for the student that wants problems that will push them to the very edge of research in probability. This book was first published in 2003. Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning, Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory. "Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning. Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided a detailed solution as well as references for preliminary and further reading. There are also many insightful notes that set the exercises in context." "Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory."--Jacket Probability theory has recently become more important as an area of study and research. This set of exercises can be used for classroom teaching or independent study and will help students reach the level where they can begin to tackle current research. It includes outline answers to all the problems and numerous references to the literature. This book presents around 100 exercises in probability. In each case, the authors have provided a detailed solution and references for preliminary and further reading. There are many insightful notes that set the exercises in context. Ideal for independent study or as companion to a course in advanced probability theory.