Description
Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs. 1 Introduction.- 2 Counting.- 2.1 order counts, with replacement.- 2.2 order counts, without replacement.- 2.3 order does not count, without replacement.- 2.4 order does not count, with replacement.- 3 Independence and Conditional Probability.- 3.1 Independence.- 3.2 Bernoulli Trials.- 3.3 The Most Likely Number of Successes.- 3.4 Conditional Probability.- 4 Random Variables.- 4.1 Expected Value and Variance.- 4.2 Computation of Expected Value and Variance.- 5 More About Random Variables.- 5.1 The Law of Large Numbers.- 5.2 Conditional Probability.- 5.3 Computation of Variance.- 6 Approximating Probabilities.- 6.1 The Poisson Distribution.- 6.2 Stirling’s Formula.- 6.3 The Normal Distribution.- 7 Generating Functions.- 8 Random Walks.- 8.1 The Probability Peter Wins.- 8.2 The Duration of Play.- 9 Markov Chains.- 9.1 What Is a Markov Chain?.- 9.2 Where Do We Get and How Often?.- 9.3 How Long Does It Take?.- 9.4 What Happens in the Long Run?.- Table of Important Distributions.- Answers.
