A Course in Probability Theory

This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

Undergraduate and graduate students studying mathematics.

Preface. Distribution Function. Measure Theory. Random Variable. Expectation. Independence. Convergence Concepts. Law of Large Numbers. Random Series. Characteristic Function. Central Limit Theorem and Its Ramifications. Random Walk. Conditioning. Markov Property. Martingale. General Bibliography. Index.