Probability with Statistical Applications

This book is intended as a one-semester first course in probability and statistics, requiring only a knowledge of calculus. It will be useful for students majoring in a number of disciplines:for example,biology, computer science, electrical engineer- ing, mathematics, and physics. Many good texts in probability and statistics are intended for a one-year course and consist of a large number of topics. In this book, the number of topics is dras- tically reduced. We concentrate instead on several important concepts that every student should understand and be able to apply in an interesting and useful way. Thus statistics is introduced at an early stage. The presentation focuses on topics in probability and statistics and tries to min- imize the difficulties students often have with calculus. Theory therefore is kept to a minimum and interesting examples are provided throughout. Chapter I contains the basic rules of probability and conditional probability with some interesting ap- plications such asBayes' rule and the birthday problem. In Chapter 2 discrete and continuous random variables, expectation and variance are introduced. This chapter is mostly computational with a few probability concepts and many applications of calculus. In Chapters 3 and 4 we get to the heart of the subject: binomial distribu- tion, normal approximation of the binomial, Poisson distribution, the Law of Large Numbers and the Central Limit Theorem. Wealso cover the Poisson approximation of the binomial (in a nonstandard way) and the Poisson scattering theorem.