This volume contains more than 1300 exercises in probability and random processes togetherwith their solutions. Apart from being a volume of worked exercises in its own right, it is alsoa solutions manual for exercises and problems appearing in the fourth edition of our textbookProbability and RandomProcesses, published by OxfordUniversity Press in 2020, henceforthreferred to as PRP. These exercises are not merely for drill, but complement and illustrate thetext of PRP, or are entertaining, or both. The current edition extends the previous edition bythe inclusion of numerous new exercises, and several new sections devoted to further topicsin aspects of stochastic processes. Since many exercises have multiple parts, the total numberof interrogatives exceeds 3000.Despite being intended in part as a companion to PRP, the present volume is as self-contained as reasonably possible. Where knowledge of a substantial chunk of bookwork isunavoidable, the reader is providedwith a reference to the relevant passage in PRP. Expressionssuch as ‘clearly’ appear frequently in the solutions. Although we do not use such terms intheir Laplacian sense to mean ‘with difficulty’, to call something ‘clear’ is not to imply thatexplicit verification is necessarily free of tedium.The table of contents reproduces that of PRP. The covered range of topics is broad,beginning with the elementary theory of probability and random variables, and continuing,via chapters on Markov chains and convergence, to extensive sections devoted to stationarityand ergodic theory, renewals, queues, martingales, and diffusions, including an introductionto the pricing of options. Generally speaking, exercises are questionswhich test knowledge ofparticular pieces of theory, while problems are less specific in their requirements. There arequestions of all standards, the great majority being elementary or of intermediate difficulty.We have found some of the later ones to be rather tricky, but have refrained from magnif