Offering a clear treatment of probability focused on problem solving, Richard Durrett presents only the essentials of probability, allowing instructors to cover this entire book in one semester. Each topic moves from the specific to the general, beginning with one or more examples that lead to theoretical results. A large number of examples and exercises relate applications to everyday life.
1. COINS, DICE, AND CARDS Experiments and Events / Probabilities / Permutations and Combinations / Urn Problems / Repeated Experiments / Probabilities of Unions / Chapter Summary and Review Problems 2. CONDITIONAL PROBABILITY Independence / Conditional Probability / Two-Stage Experiments / Bayes Formula / Recursion / Chapter Summary and Review Problems 3. DISTRIBUTIONS Examples, Poisson Approximation to Binomial / Density and Distribution Functions / Functions of Random Variables / Joint Distributions / Marginal Distributions, Independence / Functions of Several Random Variables / Sums of Independent Random Variables / Conditional Distributions / Chapter Summary and Review Problems 4. EXPECTED VALUE Examples / Moments, Generating Functions / Properties of Expectation / Variance and Covariance / Correlation / Conditional Expectation / Chapter Summary and Review Problems 5. LIMIT THEOREMS Laws of Large Numbers / The Central Limit Theorem / Confidence Intervals / Hypothesis Testing / Chapter Summary and Review Problems / ANSWERS TO SELECTED EXERCISES / FORMULAS FOR IMPORTANT DISTRIBUTIONS / TABLE OF THE NORMAL DISTRIBUTION / INDEX