40 Puzzles and Problems in Probability and Mathematical Statistics

The present book is in this tradition; it is based on the view that those cognitive skills are best acquired by solving challenging, nonstandard proba- bility problems. My own experience, both in learning and in teaching, is that challenging problems often help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The problems I selected fall into two broad categories, even though it is in the spirit of this collection that there actually is no sharp dividing line between them. Problems related to probability theory come first, followed by problems related to the application of probability in the field of mathematical statis- tics. Statistical applications are by now probably the most important reason to study probability. Thus, it seemed important to me to select problems il- lustrating in an elementary but nontrivial way that probabilistic techniques form the basis of many statistical applications. All problems seek to convey a nonstandard aspect or an approach that is not immediately obvious. plain-style deductions from abstract concepts. The problems I selected fall into two broad categories, even though it is in the spirit of this collection that there actually is no sharp dividing line between them. Problems related to probability theory come first, followed by problems related to the application of probability in the field of mathematical statis- tics. Statistical applications are by now probably the most important reason to study probability. Thus, it seemed important to me to select problems il- lustrating in an elementary but nontrivial way that probabilistic techniques form the basis of many statistical applications. All problems seek to convey a nonstandard aspect or an approach that is not immediately obvious.