This book consists of solutions to four hundred exercises, over 95% of which are in the authors Mathematical Statistics. That textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph. D. degree in statistics. On the other hand, this is a stand-alone book, since exercises and solutions are comprehensible independently of their source. Many solutions involve standard exercises that appear in other textbooks listed in the references. To help readers not using this book with Mathematical Statistics, lists of notation, terminology, and some probability distributions are given in the front of the book. Readers are assumed to have a good knowledge in advanced calculus. A course in real analysis or measure theory is highly recommended. If this book is used with a statistics textbook that does not include probability theory, then knowledge in measure-theoretic probability theory is required. The exercises are grouped into seven chapters with titles matching those in Mathematical Statistics. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison.