Problems in probability (Q2713468)

This book is a collection of exercises covering the following topics in probability theory: Sets, measure and probability, elementary probability (i.e. cards, dice, lotto, etc.), discrete and continuous random variables, limit theorems and random walks. In the first part, the problems are presented in six chapters, the second part provides the solutions. Each chapter starts with some notes, giving necessary definitions, then there are between 10 to 18 problems, most of them with several subproblems. The problems range from computing the chances of the winning numbers in lotto to proving Stirling's formula. Some of the problems are concerned with probabilistic modelling, with the validity of ``empirical rules'' in elementary statistics, or with applications in statistical quality control. In other problems the task is to write an essay on the life and work of Kolmogorov or to find counterexamples which show that some `standard assumptions' are really necessary. Most of the problems ask for proofs of statements in probability theory. The text is interspersed with historical comments and with references to sources of a problem or further information. The book is not designed to be self-contained, but it is well-suited to accompany an undergraduate course in probability theory.